public void SpringAt60DegreesInXYPlane()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D); // we will create and analyze a 2D truss system
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // also constrain it from moving in the Y axis
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(1, 1.73205); // create a second node at a distance 1 metre along the X axis and 1.73 metres along the Y axis (giving an angle of 60 degrees from x-axis).
model.ConstrainNode(node2, DegreeOfFreedom.X);
LinearConstantSpring spring = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000); // create a spring between the first two nodes of a stiffness of 1000 Newtons per metre
ForceVector force = model.ForceFactory.CreateForTruss(0, 10); // Create a force of with components of 10 Newtons along the y-axis.
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0, displacementAtNode2.X); // Check that there is no displacement in the x-axis
Assert.AreEqual(0.013333, displacementAtNode2.Z, 0.001); // and 0.01333 metres (13 millimetres) along the Y axis.
ReactionVector reactionAtNode1 = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-5.774, reactionAtNode1.X, 0.001); // Check that we have calculated a reaction of 10/SQRT(3) Newtons in the X axis.
Assert.AreEqual(-10, reactionAtNode1.Z, 0.001); // and a reaction of -10 Newtons in the Y axis.
}
public void SpringInXAxis()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D); // we will create and analyze a 1D spring in the vertical
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // also constrain it from moving in the Y axis
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(1, 0); // create a second node at a distance 1 metre along the X axis.
model.ConstrainNode(node2, DegreeOfFreedom.Z); // fix this node from moving along the Y-axis. It is still free to move along the X-axis however.
LinearConstantSpring spring = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000); // create a spring between the two nodes of a stiffness of 1000 Newtons per metre
ForceVector force = model.ForceFactory.CreateForTruss(10, 0); // Create a force of 10 Newtons along the x-axis.
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0.01, displacementAtNode2.X); // check that we calculated 0.010 metres (10 millimetres) along the Y axis.
ReactionVector reactionAtNode1 = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-10, reactionAtNode1.X); // Check that we have calculated a reaction of -10 Newtons in the X axis.
Assert.AreEqual(0, reactionAtNode1.Z); // and a reaction of 0 Newtons in the Y axis.
}
public void Cantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Beam1D); // we will create and analyze a 1D beam system
FiniteElementNode node1 = model.NodeFactory.Create(0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
model.ConstrainNode(node1, DegreeOfFreedom.YY); // constrain this node from rotating around the Y-axis
FiniteElementNode node2 = model.NodeFactory.Create(3.0); // create a second node at a distance 1 metre along the X axis
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear1DBeam(node1, node2, material, section);
ForceVector force = model.ForceFactory.CreateFor1DBeam(-10000, 0); // Create a force of 10 KiloNewtons in the z direction
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
ReactionVector reaction = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(10000, reaction.Z, 0.001); // Check that we have calculated a reaction of 10 KiloNewtons in the Z-axis
Assert.AreEqual(-30000, reaction.YY, 0.001); // Check that we have calculated a reaction of -30 KiloNewtonMetres around the YY axis.
DisplacementVector displacement = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(-0.00214, displacement.Z, 0.0005);
Assert.AreEqual(0.00107, displacement.YY, 0.0001);
}
public void ReversedCantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Beam1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.Create(3.0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear1DBeam(node2, node1, material, section); //connecting the nodes in reverse order to the Cantilever() example
ForceVector force = model.ForceFactory.CreateFor1DBeam(-10000, 0);
model.ApplyForceToNode(force, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction = results.GetReaction(node1);
Assert.AreEqual(10000, reaction.Z, 0.001);
Assert.AreEqual(-30000, reaction.YY, 0.001);
DisplacementVector displacement = results.GetDisplacement(node2);
Assert.AreEqual(-0.00214, displacement.Z, 0.0005);
Assert.AreEqual(0.00107, displacement.YY, 0.0001);
}
public void OneVerticalQuadFixed3PointsMembrane()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 0.0, 1.0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 0.0, 1.0);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
ForceVector force = model.ForceFactory.Create(10000, 0, 0, 0, 0, 0);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction3 = results.GetReaction(node3);
Console.WriteLine("\nReaction3 : \n" + reaction3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual(2621, reaction1.X, 1);
Assert.AreEqual(-3039, reaction1.Z, 1);
Assert.AreEqual(-5660, reaction2.X, 1);
Assert.AreEqual(1706, reaction2.Z, 1);
Assert.AreEqual(-6961, reaction3.X, 1);
Assert.AreEqual(1333, reaction3.Z, 1);
Assert.AreEqual(0.0000012400, displacement4.X, 0.0000000001);
Assert.AreEqual(0.0000004875, displacement4.Z, 0.0000000001);
}
public void Calculate2DPortalFrameOf3BeamsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(-3, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.Create(-3, 0, 6);
FiniteElementNode node3 = model.NodeFactory.Create(3, 0, 6);
FiniteElementNode node4 = model.NodeFactory.Create(3, 0, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.XX);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000);
ICrossSection section = new GenericCrossSection(0.0002, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node4, material, section);
ForceVector force2 = model.ForceFactory.Create(15000, 0, 0, 0, -10000, 0);
model.ApplyForceToNode(force2, node2);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node2Displacement = results.GetDisplacement(node2);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node4Reaction = results.GetReaction(node4);
Assert.AreEqual(0.0052843, node2Displacement.X, 0.0001);
Assert.AreEqual(0.0006522, node2Displacement.Z, 0.0001);
Assert.AreEqual(0.0005, node2Displacement.YY, 0.0001);
Assert.AreEqual(0.0044052, node3Displacement.X, 0.0001);
Assert.AreEqual(-0.0006522, node3Displacement.Z, 0.0001);
Assert.AreEqual(0.0006, node3Displacement.YY, 0.0001);
Assert.AreEqual(-9000, node1Reaction.X, 500);
Assert.AreEqual(-5000, node1Reaction.Z, 500);
Assert.AreEqual(-30022, node1Reaction.YY, 500);
Assert.AreEqual(-6000, node4Reaction.X, 500);
Assert.AreEqual(5000, node4Reaction.Z, 500);
Assert.AreEqual(-22586, node4Reaction.YY, 500);
}
public void Calculate2DFrameOf3BeamsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 3);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.Create(3, 0, 3);
FiniteElementNode node3 = model.NodeFactory.Create(6, 0, 0);
FiniteElementNode node4 = model.NodeFactory.Create(9, 0, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.XX);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node4, material, section);
ForceVector force2 = model.ForceFactory.Create(0, 0, -10000, 0, 5000, 0);
model.ApplyForceToNode(force2, node2);
ForceVector force3 = model.ForceFactory.Create(0, 0, -10000, 0, -5000, 0);
model.ApplyForceToNode(force3, node3);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node2Displacement = results.GetDisplacement(node2);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node4Reaction = results.GetReaction(node4);
Assert.AreEqual(0, node2Displacement.X, 0.0001);
Assert.AreEqual(-0.0013496, node2Displacement.Z, 0.0001); ///NOTE this value of -0.0013496 matches the example, but -0.0314233 was calculated using a commercial finite element software
Assert.AreEqual(0.00059173, node2Displacement.YY, 0.0001); ///NOTE this value of 0.00059173 does not match the example, but was verified using a commercial finite element software
Assert.AreEqual(0, node3Displacement.X, 0.0001);
Assert.AreEqual(-0.0013496, node3Displacement.Z, 0.0001); ///NOTE this value matches the example, but was verified using a commercial finite element software
Assert.AreEqual(-0.00059173, node3Displacement.YY, 0.0001); ///NOTE this value of -0.00059173 does not match the example, but was verified using a commercial finite element software
Assert.AreEqual(0, node1Reaction.X, 1);
Assert.AreEqual(10000, node1Reaction.Z, 1);
Assert.AreEqual(-23284, node1Reaction.YY, 1); ///NOTE this value of -23284 does not match the example, but was verified using a commercial finite element software
Assert.AreEqual(0, node4Reaction.X, 1);
Assert.AreEqual(10000, node4Reaction.Z, 1);
Assert.AreEqual(23284, node4Reaction.YY, 1); ///NOTE this value of 23284 does not match the example, but was verified using a commercial finite element software
}
public void ThreeNodeSimplySupportedBeam() //TODO verify results using independent check
{
FiniteElementModel model = new FiniteElementModel(ModelType.Frame2D);
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(1, 0);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(2, 0);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 10000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear1DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear1DBeam(node2, node3, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
Stiffness.GlobalModelStiffnessMatrixBuilder gmsmb = new SharpFE.Stiffness.GlobalModelStiffnessMatrixBuilder(model);
Console.WriteLine(gmsmb.BuildKnownForcesUnknownDisplacementStiffnessMatrix());
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
Console.WriteLine("node1Displacement : " + node1Displacement);
DisplacementVector node2Displacement = results.GetDisplacement(node2);
Console.WriteLine("node2Displacement : " + node2Displacement);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
Console.WriteLine("node3Displacement : " + node3Displacement);
ReactionVector node1Reaction = results.GetReaction(node1);
Console.WriteLine("node1Reaction : " + node1Reaction);
ReactionVector node3Reaction = results.GetReaction(node3);
Console.WriteLine("node5Reaction : " + node3Reaction);
Assert.AreEqual(-0.000833333, node2Displacement.Z, 0.0000001);
Assert.AreEqual(5000, node1Reaction.Z, 0.001);
Assert.AreEqual(5000, node3Reaction.Z, 0.001);
Assert.AreEqual(0, node2Displacement.YY, 0.0001);
Assert.AreEqual(0.00125, node1Displacement.YY, 0.0000001);
Assert.AreEqual(-0.00125, node3Displacement.YY, 0.0000001);
}
public void CalculateGridOf3BeamsAnd24Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Slab2D);
FiniteElementNode node1 = model.NodeFactory.Create(4, 4);
FiniteElementNode node2 = model.NodeFactory.Create(4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.XX);
model.ConstrainNode(node2, DegreeOfFreedom.YY);
FiniteElementNode node3 = model.NodeFactory.Create(0, 0);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
model.ConstrainNode(node3, DegreeOfFreedom.XX);
model.ConstrainNode(node3, DegreeOfFreedom.YY);
FiniteElementNode node4 = model.NodeFactory.Create(0, 4);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.XX);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node4, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -20000, 0, 0, 0);
model.ApplyForceToNode(force, node1);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
Assert.AreEqual(-0.0033, node1Displacement.Z, 0.0001);
Assert.AreEqual(-0.0010, node1Displacement.XX, 0.0001);
Assert.AreEqual(0.0010, node1Displacement.YY, 0.0001);
Assert.AreEqual(10794, node2Reaction.Z, 1);
Assert.AreEqual(31776, node2Reaction.XX, 1);
Assert.AreEqual(-1019, node2Reaction.YY, 1);
Assert.AreEqual(-1587, node3Reaction.Z, 1);
Assert.AreEqual(4030, node3Reaction.XX, 1);
Assert.AreEqual(-4030, node3Reaction.YY, 1);
Assert.AreEqual(10794, node4Reaction.Z, 1);
Assert.AreEqual(1019, node4Reaction.XX, 1);
Assert.AreEqual(-31776, node4Reaction.YY, 1);
}
public void Calculate3DFrameOf3BeamsAnd24Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
FiniteElementNode node2 = model.NodeFactory.Create(3, 0, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 3, 0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0, 0, -4);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0001, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node4, material, section);
ForceVector force = model.ForceFactory.Create(-10000, -15000, 0, 0, 0, 0);
model.ApplyForceToNode(force, node1);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
Console.WriteLine("\nNode1 displacement : \n" + node1Displacement);
Console.WriteLine("\nNode2 reaction : \n" + node2Reaction);
Console.WriteLine("\nNode3 reaction : \n" + node3Reaction);
Console.WriteLine("\nNode4 reaction : \n" + node4Reaction);
Assert.Inconclusive("The below x, y and zz pass, but z, xx, yy fail");
Assert.AreEqual(-0.000007109, node1Displacement.X, 0.00000001);
Assert.AreEqual(-0.000010680, node1Displacement.Y, 0.00000001);
Assert.AreEqual(-0.000014704, node1Displacement.Z, 0.00000001);
Assert.AreEqual(0.000001147, node1Displacement.XX, 0.00000001);
Assert.AreEqual(-0.000001068, node1Displacement.YY, 0.00000001);
Assert.AreEqual(0.000000595, node1Displacement.ZZ, 0.000000001);
}
public void TwoTriangleWall()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D); // we will create and analyze a 2D slab system
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain the node from moving in the x-axis
model.ConstrainNode(node1, DegreeOfFreedom.Y); // constrain the node from moving in the y-axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0); // create a second node at a distance 1 metre along the X axis
model.ConstrainNode(node2, DegreeOfFreedom.X); // constrain the node from moving in the x-axis
model.ConstrainNode(node2, DegreeOfFreedom.Y); // constrain the node from moving in the y-axis
model.ConstrainNode(node2, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node3 = model.NodeFactory.Create(0.0, 1.0, 0.0);
model.ConstrainNode(node3, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node4 = model.NodeFactory.Create(1.0, 1.0, 0.0);
model.ConstrainNode(node4, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
IMaterial material = new GenericElasticMaterial(0, 200000, 0.2, 84000);
model.ElementFactory.CreateLinearConstantStrainTriangle(node1, node2, node3, material, 0.1); // create a triangle of thickness of 0.1 metres
model.ElementFactory.CreateLinearConstantStrainTriangle(node2, node4, node3, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, -10); // Create a force of 10 Newtons in the y direction
model.ApplyForceToNode(force, node3); // Apply that force to the third node
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1); //get the reaction at the first node
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20, reaction1.Y + reaction2.Y, 0.001);
DisplacementVector displacement3 = results.GetDisplacement(node3); // get the displacement at the second node
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Assert.AreNotEqual(0.0, displacement3.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreEqual(0.0, displacement3.Z); // TODO calculate the actual value, rather than just checking we have any value
DisplacementVector displacement4 = results.GetDisplacement(node4); // get the displacement at the second node
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreNotEqual(0.0, displacement4.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreEqual(0.0, displacement4.Z); // TODO calculate the actual value, rather than just checking we have any value
}
public void Setup()
{
SUT = new FiniteElementModel(ModelType.Truss1D);
node1 = SUT.NodeFactory.Create(0);
node2 = SUT.NodeFactory.Create(1);
node3 = SUT.NodeFactory.Create(2);
spring1 = SUT.ElementFactory.CreateLinearConstantSpring(node1, node2, 3);
spring2 = SUT.ElementFactory.CreateLinearConstantSpring(node2, node3, 2);
SUT.ConstrainNode(node1, DegreeOfFreedom.X);
SUT.ConstrainNode(node3, DegreeOfFreedom.X);
force1 = SUT.ForceFactory.Create(20);
SUT.ApplyForceToNode(force1, node2);
}
public void CalculateModelOfOneSpringWith2DegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D); // we will create and analyze a 1D truss system
FiniteElementNode node1 = model.NodeFactory.Create(0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0); // create a second node at a distance 1 metre along the X axis
model.ElementFactory.CreateLinearConstantSpring(node1, node2, 2000.0); // create a spring between the two nodes of a stiffness of 2000 Newtons per metre
ForceVector force = model.ForceFactory.Create(10.0); // Create a force of 10 Newtons in the x direction
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacement = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0.005, displacement.X); // Check that we have calculated a displacement of 0.005 metres (5 millimetres) along the X axis.
ReactionVector reaction = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-10, reaction.X); // Check that we have calculated a reaction of -10 Newtons in the X axis.
}
public void OneQuadMembraneLateralLoad()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane2D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 1.0);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 1.0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
ForceVector force = model.ForceFactory.Create(10000, 0);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
// Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
// Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(0, reaction1.Y + reaction2.Y, 1);
Assert.AreEqual(-10000, reaction1.X, 1);
DisplacementVector displacement3 = results.GetDisplacement(node3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual(0.000002619047, displacement3.X, 0.0000000001);
Assert.AreEqual(-0.000001428571, displacement3.Y, 0.0000000001);
Assert.AreEqual(0.000004047618, displacement4.X, 0.0000000001);
Assert.AreEqual(0.000001428571, displacement4.Y, 0.0000000001);
}
public void Calculate3DFrameOf3BeamsAnd24Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
FiniteElementNode node2 = model.NodeFactory.Create(3, 0, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 3, 0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0, 0, -4);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0001, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node4, material, section);
ForceVector force = model.ForceFactory.Create(-10000, -15000, 0, 0, 0, 0);
model.ApplyForceToNode(force, node1);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
Console.WriteLine("\nNode1 displacement : \n" + node1Displacement);
Console.WriteLine("\nNode2 reaction : \n" + node2Reaction);
Console.WriteLine("\nNode3 reaction : \n" + node3Reaction);
Console.WriteLine("\nNode4 reaction : \n" + node4Reaction);
Assert.Inconclusive("The below x, y and zz pass, but z, xx, yy fail");
Assert.AreEqual(-0.000007109, node1Displacement.X, 0.00000001);
Assert.AreEqual(-0.000010680, node1Displacement.Y, 0.00000001);
Assert.AreEqual(-0.000014704, node1Displacement.Z, 0.00000001);
Assert.AreEqual(0.000001147, node1Displacement.XX, 0.00000001);
Assert.AreEqual(-0.000001068, node1Displacement.YY, 0.00000001);
Assert.AreEqual(0.000000595, node1Displacement.ZZ, 0.000000001);
}
public void CalculateModelOfTwoBarsAndOneSpringWithFourDegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
FiniteElementNode node2 = model.NodeFactory.Create(2.0);
FiniteElementNode node3 = model.NodeFactory.Create(4.0);
FiniteElementNode node4 = model.NodeFactory.Create(6.0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
IMaterial material = new GenericElasticMaterial(0, 70000000000, 0, 0);
ICrossSection section = new SolidRectangle(0.02, 0.01);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node2, node3, material, section);
model.ElementFactory.CreateLinearConstantSpring(node3, node4, 2000000);
ForceVector externalForce = model.ForceFactory.Create(8000);
model.ApplyForceToNode(externalForce, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0.000935, displacementAtNode2.X, 0.001);
DisplacementVector displacementAtNode3 = results.GetDisplacement(node3);
Assert.AreEqual(0.000727, displacementAtNode3.X, 0.001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-6546, reactionAtNode1.X, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-1455, reactionAtNode4.X, 1);
}
private void Create2DSingleSpringModelAroundOrigin(double x, double z)
{
model = new FiniteElementModel(ModelType.Truss2D);
node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
node2 = model.NodeFactory.CreateFor2DTruss(x, z);
spring1 = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.X);
force1 = model.ForceFactory.CreateForTruss(0, -10);
model.ApplyForceToNode(force1, node2);
SUT = new LinearSolverSVD(model);
}
public void CalculateModelOfThreeSpringsWithFourDegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
FiniteElementNode node2 = model.NodeFactory.Create(1.0);
FiniteElementNode node3 = model.NodeFactory.Create(2.0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
FiniteElementNode node4 = model.NodeFactory.Create(2.00001); ///TODO allow multiple nodes to be added in the same location
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1);
model.ElementFactory.CreateLinearConstantSpring(node2, node3, 1);
model.ElementFactory.CreateLinearConstantSpring(node2, node4, 1);
ForceVector externalForce = model.ForceFactory.Create(10);
model.ApplyForceToNode(externalForce, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(3.333, displacementAtNode2.X, 0.001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-3.333, reactionAtNode1.X, 0.001);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(-3.333, reactionAtNode3.X, 0.001);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-3.333, reactionAtNode4.X, 0.001);
}
public void SimplySupportedBeam() //TODO verify using independent check
{
FiniteElementModel model = new FiniteElementModel(ModelType.Beam1D); // we will create and analyze a 1D beam system
FiniteElementNode node1 = model.NodeFactory.Create(0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0); // create a second node at a distance 1 metre along the X axis
model.ConstrainNode(node2, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section); // create a spring between the two nodes of a stiffness of 2000 Newtons per metre
ForceVector moment = model.ForceFactory.CreateFor1DBeam(0, 10000); // Create a clockwise(?) moment of 10 KiloNewtonmetres around the yy axis
model.ApplyForceToNode(moment, node1); // Apply that moment to the first node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
// check the results
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(0, displacementAtNode1.Z, 0.001);
Assert.AreEqual(0.00007936, displacementAtNode1.YY, 0.00000001);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0, displacementAtNode2.Z, 0.001);
Assert.AreEqual(-0.00003968, displacementAtNode2.YY, 0.00000001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-10000, reactionAtNode1.Z, 0.001);
Assert.AreEqual(0, reactionAtNode1.YY, 0.001);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(10000, reactionAtNode2.Z, 0.001);
Assert.AreEqual(0, reactionAtNode2.YY, 0.001);
}
public void OneQuadMembraneLateralLoad()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane2D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 1.0);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 1.0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
ForceVector force = model.ForceFactory.Create(10000, 0);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
// Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
// Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(0, reaction1.Y + reaction2.Y, 1);
Assert.AreEqual(-10000, reaction1.X, 1);
DisplacementVector displacement3 = results.GetDisplacement(node3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual( 0.000002619047, displacement3.X, 0.0000000001);
Assert.AreEqual(-0.000001428571, displacement3.Y, 0.0000000001);
Assert.AreEqual( 0.000004047618, displacement4.X, 0.0000000001);
Assert.AreEqual( 0.000001428571, displacement4.Y, 0.0000000001);
}
public void SimplySupportedBeam()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.XX);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
ForceVector moment = model.ForceFactory.Create(0, 0, 0, 0, 10000, 0);
model.ApplyForceToNode(moment, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
// check the results
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(0, displacementAtNode1.Z, 0.001);
Assert.AreEqual(0.00007936, displacementAtNode1.YY, 0.000001);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0, displacementAtNode2.Z, 0.001);
Assert.AreEqual(-0.00003968, displacementAtNode2.YY, 0.000001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-10000, reactionAtNode1.Z, 0.001);
Assert.AreEqual(0, reactionAtNode1.YY, 0.001);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(10000, reactionAtNode2.Z, 0.001);
Assert.AreEqual(0, reactionAtNode2.YY, 0.001);
}
public void CalculateModelOfThreeBarsWithFourDegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
FiniteElementNode node2 = model.NodeFactory.Create(30.0);
FiniteElementNode node3 = model.NodeFactory.Create(60.0);
FiniteElementNode node4 = model.NodeFactory.Create(90.0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
IMaterial material = new GenericElasticMaterial(0, 30000000, 0, 0);
ICrossSection section = new SolidRectangle(1, 1);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node2, node3, material, section);
model.ElementFactory.CreateLinearTruss(node3, node4, material, section);
ForceVector externalForce = model.ForceFactory.Create(3000);
model.ApplyForceToNode(externalForce, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0.002, displacementAtNode2.X, 0.001);
DisplacementVector displacementAtNode3 = results.GetDisplacement(node3);
Assert.AreEqual(0.001, displacementAtNode3.X, 0.001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-2000, reactionAtNode1.X, 0.001);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-1000, reactionAtNode4.X, 0.001);
}
public void SetUp()
{
model = new FiniteElementModel(ModelType.Truss1D);
node1 = model.NodeFactory.Create(0);
node2 = model.NodeFactory.Create(1);
spring1 = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 4);
model.ConstrainNode(node1, DegreeOfFreedom.X);
force1 = model.ForceFactory.Create(20);
model.ApplyForceToNode(force1, node2);
SUT = new LinearSolverSVD(model);
}
public void SetUp()
{
model = new FiniteElementModel(ModelType.Truss1D);
node1 = model.NodeFactory.Create(0);
node2 = model.NodeFactory.Create(1);
spring1 = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 4);
model.ConstrainNode(node1, DegreeOfFreedom.X);
force1 = model.ForceFactory.Create(20);
model.ApplyForceToNode(force1, node2);
SUT = new LinearSolverSVD(model);
}
public void Calculate2DTrussOf3BarsAnd8Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D);
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(0, 10);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(10, 10);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(10, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 30000000, 0, 0);
ICrossSection section = new SolidRectangle(2, 1);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
ForceVector externalForce = model.ForceFactory.CreateForTruss(0, -10000);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(0, reactionAtNode2.X, 1);
Assert.AreEqual(7929, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(2071, reactionAtNode3.X, 1);
Assert.AreEqual(2071, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-2071, reactionAtNode4.X, 1);
Assert.AreEqual(0, reactionAtNode4.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(0.00035, displacementAtNode1.X, 0.00001); ///NOTE this does not match the example in the book, but was instead verified by commercial FE software. It appears as it may be an errata in the book.
Assert.AreEqual(-0.00132, displacementAtNode1.Z, 0.00001); ///NOTE this does not match the example in the book, but was instead verified by commercial FE software. It appears as it may be an errata in the book.
}
public void CalculateModelOfOneSpringWith2DegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D); // we will create and analyze a 1D truss system
FiniteElementNode node1 = model.NodeFactory.Create(0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0); // create a second node at a distance 1 metre along the X axis
model.ElementFactory.CreateLinearConstantSpring(node1, node2, 2000.0); // create a spring between the two nodes of a stiffness of 2000 Newtons per metre
ForceVector force = model.ForceFactory.Create(10.0); // Create a force of 10 Newtons in the x direction
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacement = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0.005, displacement.X); // Check that we have calculated a displacement of 0.005 metres (5 millimetres) along the X axis.
ReactionVector reaction = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-10, reaction.X); // Check that we have calculated a reaction of -10 Newtons in the X axis.
}
public void ThreeNodeCantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
model.ConstrainNode(node1, DegreeOfFreedom.ZZ);
FiniteElementNode node2 = model.NodeFactory.Create(1.5, 0, 0);
FiniteElementNode node3 = model.NodeFactory.Create(3.0, 0, 0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction = results.GetReaction(node1);
Assert.AreEqual(10000, reaction.Z, 0.001);
Assert.AreEqual(-30000, reaction.YY, 0.001);
DisplacementVector displacement2 = results.GetDisplacement(node2);
Assert.AreEqual(-0.000670, displacement2.Z, 0.0005);
Assert.AreEqual(0.000804, displacement2.YY, 0.0001);
DisplacementVector displacement3 = results.GetDisplacement(node3);
Assert.AreEqual(-0.00214, displacement3.Z, 0.0005);
Assert.AreEqual(0.00107, displacement3.YY, 0.0001);
}
public void Cantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D); // we will create and analyze a 1D beam system
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY); // constrain this node from rotating around the Y-axis
model.ConstrainNode(node1, DegreeOfFreedom.ZZ);
FiniteElementNode node2 = model.NodeFactory.Create(3.0, 0, 0); // create a second node at a distance 1 metre along the X axis
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0); // Create a force of 10 KiloNewtons in the z direction
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
ReactionVector reaction = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(10000, reaction.Z, 0.001); // Check that we have calculated a reaction of 10 KiloNewtons in the Z-axis
Assert.AreEqual(-30000, reaction.YY, 0.001); // Check that we have calculated a reaction of -30 KiloNewtonMetres around the YY axis.
DisplacementVector displacement = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(-0.00214, displacement.Z, 0.0005);
Assert.AreEqual(0.00107, displacement.YY, 0.0001);
}
public void Calculate3DTrussOf3BarsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss3D);
FiniteElementNode node1 = model.NodeFactory.Create(72, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
FiniteElementNode node2 = model.NodeFactory.Create(0, 36, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 36, 72);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0, 0, -48);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 1200000, 0, 0);
ICrossSection section1 = new SolidRectangle(1, 0.302);
ICrossSection section2 = new SolidRectangle(1, 0.729); ///NOTE example also refers to this as A1. Assume errata in book
ICrossSection section3 = new SolidRectangle(1, 0.187); ///NOTE example also refers to this as A1. Assume errata in book
model.ElementFactory.CreateLinearTruss(node1, node2, material, section1);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section2);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section3);
ForceVector externalForce = model.ForceFactory.Create(0, 0, -1000, 0, 0, 0);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode1.X, 1);
Assert.AreEqual(-223.1632, reactionAtNode1.Y, 1);
Assert.AreEqual(0, reactionAtNode1.Z, 1);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(256.1226, reactionAtNode2.X, 1);
Assert.AreEqual(-128.0613, reactionAtNode2.Y, 1);
Assert.AreEqual(0, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(-702.4491, reactionAtNode3.X, 1);
Assert.AreEqual(351.2245, reactionAtNode3.Y, 1);
Assert.AreEqual(702.4491, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(446.3264, reactionAtNode4.X, 1);
Assert.AreEqual(0, reactionAtNode4.Y, 1);
Assert.AreEqual(297.5509, reactionAtNode4.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(-0.0711, displacementAtNode1.X, 0.0001);
Assert.AreEqual(0, displacementAtNode1.Y, 0.0001);
Assert.AreEqual(-0.2662, displacementAtNode1.Z, 0.0001);
}
public void OneVerticalQuadFixed3PointsMembrane()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 0.0, 1.0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 0.0, 1.0);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
ForceVector force = model.ForceFactory.Create(10000, 0, 0, 0, 0, 0);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction3 = results.GetReaction(node3);
Console.WriteLine("\nReaction3 : \n" + reaction3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual( 2621, reaction1.X, 1);
Assert.AreEqual(-3039, reaction1.Z, 1);
Assert.AreEqual(-5660, reaction2.X, 1);
Assert.AreEqual( 1706, reaction2.Z, 1);
Assert.AreEqual(-6961, reaction3.X, 1);
Assert.AreEqual( 1333, reaction3.Z, 1);
Assert.AreEqual( 0.0000012400, displacement4.X, 0.0000000001);
Assert.AreEqual( 0.0000004875, displacement4.Z, 0.0000000001);
}
public void QuadMembraneAFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 1.0, 1.0);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 1.0, 1.0);
FiniteElementNode node5 = model.NodeFactory.Create(1.0, 2.0, 0.0);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.Create(0.0, 2.0, 0.0);
model.ConstrainNode(node6, DegreeOfFreedom.X);
model.ConstrainNode(node6, DegreeOfFreedom.Y);
model.ConstrainNode(node6, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node5, node6, node4, node3, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction5 = results.GetReaction(node5);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction6 = results.GetReaction(node6);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20000, reaction1.Z + reaction2.Z + reaction5.Z + reaction6.Z, 1);
DisplacementVector displacement3 = results.GetDisplacement(node3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual( 0.0000002020, displacement3.X, 0.0000000001);
Assert.AreEqual( 0, displacement3.Y, 0.0000000001);
Assert.AreEqual(-0.0000013469, displacement3.Z, 0.0000000001);
Assert.AreEqual(0, displacement4.X, 0.0000000001);
Assert.AreEqual(0, displacement4.Y, 0.0000000001);
Assert.AreEqual(-0.0000013469, displacement4.Z, 0.0000000001);
}
public void AnalyzeSimple2DFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D);
//build geometric model and constraints
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(0, 3);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(3, 0);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(3, 3);
FiniteElementNode node5 = model.NodeFactory.CreateFor2DTruss(6, 0);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.CreateFor2DTruss(6, 3);
IMaterial material = new GenericElasticMaterial(0, 70000000, 0, 0);
ICrossSection section = new SolidRectangle(0.03, 0.01);
LinearTruss truss1 = model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
LinearTruss truss2 = model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
LinearTruss truss3 = model.ElementFactory.CreateLinearTruss(node2, node3, material, section);
LinearTruss truss4 = model.ElementFactory.CreateLinearTruss(node2, node4, material, section);
LinearTruss truss5 = model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
LinearTruss truss6 = model.ElementFactory.CreateLinearTruss(node3, node4, material, section);
LinearTruss truss7 = model.ElementFactory.CreateLinearTruss(node3, node6, material, section);
LinearTruss truss8 = model.ElementFactory.CreateLinearTruss(node4, node5, material, section);
LinearTruss truss9 = model.ElementFactory.CreateLinearTruss(node4, node6, material, section);
LinearTruss truss10 = model.ElementFactory.CreateLinearTruss(node3, node5, material, section);
LinearTruss truss11 = model.ElementFactory.CreateLinearTruss(node5, node6, material, section);
//apply forces
ForceVector force50Z = model.ForceFactory.CreateForTruss(0, -50000);
model.ApplyForceToNode(force50Z, node2);
model.ApplyForceToNode(force50Z, node6);
ForceVector force100Z = model.ForceFactory.CreateForTruss(0, -100000);
model.ApplyForceToNode(force100Z, node4);
//solve model
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
//assert results
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode1.X, 1);
Assert.AreEqual(100000, reactionAtNode1.Z, 1);
ReactionVector reactionAtNode5 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode5.X, 1);
Assert.AreEqual(100000, reactionAtNode5.Z, 1);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(7.1429, displacementAtNode2.X, 0.001);
Assert.AreEqual(-9.0386, displacementAtNode2.Z, 0.001);
DisplacementVector displacementAtNode3 = results.GetDisplacement(node3);
Assert.AreEqual(5.2471, displacementAtNode3.X, 0.001);
Assert.AreEqual(-16.2965, displacementAtNode3.Z, 0.001);
DisplacementVector displacementAtNode4 = results.GetDisplacement(node4);
Assert.AreEqual(5.2471, displacementAtNode4.X, 0.001);
Assert.AreEqual(-20.0881, displacementAtNode4.Z, 0.001);
DisplacementVector displacementAtNode5 = results.GetDisplacement(node5);
Assert.AreEqual(10.4942, displacementAtNode5.X, 0.001);
Assert.AreEqual(0, displacementAtNode5.Z, 0.001);
DisplacementVector displacementAtNode6 = results.GetDisplacement(node6);
Assert.AreEqual(3.3513, displacementAtNode6.X, 0.001);
Assert.AreEqual(-9.0386, displacementAtNode6.Z, 0.001);
}
public void SimplySupportedBeam()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Beam1D); // we will create and analyze a 1D beam system
FiniteElementNode node1 = model.NodeFactory.Create(0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0); // create a second node at a distance 1 metre along the X axis
model.ConstrainNode(node2, DegreeOfFreedom.Z); // constrain the node from moving in the Z-axis
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section); // create a spring between the two nodes of a stiffness of 2000 Newtons per metre
ForceVector moment = model.ForceFactory.CreateFor1DBeam(0, 10000); // Create a clockwise(?) moment of 10 KiloNewtonmetres around the yy axis
model.ApplyForceToNode(moment, node1); // Apply that moment to the first node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
// check the results
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(0, displacementAtNode1.Z, 0.001);
Assert.AreEqual(0.00007936, displacementAtNode1.YY, 0.00000001);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0, displacementAtNode2.Z, 0.001);
Assert.AreEqual(-0.00003968, displacementAtNode2.YY, 0.00000001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-10000, reactionAtNode1.Z, 0.001);
Assert.AreEqual(0, reactionAtNode1.YY, 0.001);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(10000, reactionAtNode2.Z, 0.001);
Assert.AreEqual(0, reactionAtNode2.YY, 0.001);
}
public void Calculate2DPortalFrameOf3BeamsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(-3, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.Create(-3, 0, 6);
FiniteElementNode node3 = model.NodeFactory.Create(3, 0, 6);
FiniteElementNode node4 = model.NodeFactory.Create(3, 0, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.XX);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000);
ICrossSection section = new GenericCrossSection(0.0002, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node4, material, section);
ForceVector force2 = model.ForceFactory.Create(15000, 0, 0, 0, -10000, 0);
model.ApplyForceToNode(force2, node2);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node2Displacement = results.GetDisplacement(node2);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node4Reaction = results.GetReaction(node4);
Assert.AreEqual(0.0052843, node2Displacement.X, 0.0001);
Assert.AreEqual(0.0006522, node2Displacement.Z, 0.0001);
Assert.AreEqual(0.0005, node2Displacement.YY, 0.0001);
Assert.AreEqual(0.0044052, node3Displacement.X, 0.0001);
Assert.AreEqual(-0.0006522, node3Displacement.Z, 0.0001);
Assert.AreEqual(0.0006, node3Displacement.YY, 0.0001);
Assert.AreEqual(-9000, node1Reaction.X, 500);
Assert.AreEqual(-5000, node1Reaction.Z, 500);
Assert.AreEqual(-30022, node1Reaction.YY, 500);
Assert.AreEqual(-6000, node4Reaction.X, 500);
Assert.AreEqual(5000, node4Reaction.Z, 500);
Assert.AreEqual(-22586, node4Reaction.YY, 500);
}
public void ThreeNodeCantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
model.ConstrainNode(node1, DegreeOfFreedom.ZZ);
FiniteElementNode node2 = model.NodeFactory.Create(1.5, 0, 0);
FiniteElementNode node3 = model.NodeFactory.Create(3.0, 0, 0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction = results.GetReaction(node1);
Assert.AreEqual(10000, reaction.Z, 0.001);
Assert.AreEqual(-30000, reaction.YY, 0.001);
DisplacementVector displacement2 = results.GetDisplacement(node2);
Assert.AreEqual(-0.000670, displacement2.Z, 0.0005);
Assert.AreEqual(0.000804, displacement2.YY, 0.0001);
DisplacementVector displacement3 = results.GetDisplacement(node3);
Assert.AreEqual(-0.00214, displacement3.Z, 0.0005);
Assert.AreEqual(0.00107, displacement3.YY, 0.0001);
}
public void Calculate3DTrussOf4BarsAnd15Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss3D);
FiniteElementNode node1 = model.NodeFactory.Create(4, 4, 3);
FiniteElementNode node2 = model.NodeFactory.Create(0, 4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 4, 6);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(4, 0, 3);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
FiniteElementNode node5 = model.NodeFactory.Create(8, -1, 1);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new SolidRectangle(0.01, 0.01);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
model.ElementFactory.CreateLinearTruss(node1, node5, material, section);
ForceVector externalForce = model.ForceFactory.Create(0, -10000, 0, 0, 0, 0);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(270.9, reactionAtNode2.X, 1);
Assert.AreEqual(0, reactionAtNode2.Y, 1);
Assert.AreEqual(203.2, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(1354.6, reactionAtNode3.X, 1);
Assert.AreEqual(0, reactionAtNode3.Y, 1);
Assert.AreEqual(-1016, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(0, reactionAtNode4.X, 1);
Assert.AreEqual(7968.1, reactionAtNode4.Y, 1);
Assert.AreEqual(0, reactionAtNode4.Z, 1);
ReactionVector reactionAtNode5 = results.GetReaction(node5);
Assert.AreEqual(-1625.5, reactionAtNode5.X, 1);
Assert.AreEqual(2031.9, reactionAtNode5.Y, 1);
Assert.AreEqual(812.8, reactionAtNode5.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(-0.0003024, displacementAtNode1.X, 0.0001); //NOTE the results given in the book are 1E03
Assert.AreEqual(-0.0015177, displacementAtNode1.Y, 0.0001);
Assert.AreEqual(0.0002688, displacementAtNode1.Z, 0.0001);
}
public void CalculateGridOf3BeamsAnd24Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Slab2D);
FiniteElementNode node1 = model.NodeFactory.Create(4, 4);
FiniteElementNode node2 = model.NodeFactory.Create(4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.XX);
model.ConstrainNode(node2, DegreeOfFreedom.YY);
FiniteElementNode node3 = model.NodeFactory.Create(0, 0);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
model.ConstrainNode(node3, DegreeOfFreedom.XX);
model.ConstrainNode(node3, DegreeOfFreedom.YY);
FiniteElementNode node4 = model.NodeFactory.Create(0, 4);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.XX);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node1, node4, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -20000, 0, 0, 0);
model.ApplyForceToNode(force, node1);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
Assert.AreEqual(-0.0033, node1Displacement.Z, 0.0001);
Assert.AreEqual(-0.0010, node1Displacement.XX, 0.0001);
Assert.AreEqual( 0.0010, node1Displacement.YY, 0.0001);
Assert.AreEqual(10794, node2Reaction.Z, 1);
Assert.AreEqual(31776, node2Reaction.XX, 1);
Assert.AreEqual(-1019, node2Reaction.YY, 1);
Assert.AreEqual(-1587, node3Reaction.Z, 1);
Assert.AreEqual(4030, node3Reaction.XX, 1);
Assert.AreEqual(-4030, node3Reaction.YY, 1);
Assert.AreEqual(10794, node4Reaction.Z, 1);
Assert.AreEqual(1019, node4Reaction.XX, 1);
Assert.AreEqual(-31776, node4Reaction.YY, 1);
}
public void FourTriangleAFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0.0, 1.0, 0.5);
FiniteElementNode node4 = model.NodeFactory.Create(1.0, 1.0, 0.5);
FiniteElementNode node5 = model.NodeFactory.Create(0.0, 2.0, 0.0);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.Create(1.0, 2.0, 0.0);
model.ConstrainNode(node6, DegreeOfFreedom.X);
model.ConstrainNode(node6, DegreeOfFreedom.Y);
model.ConstrainNode(node6, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 200000, 0.2, 84000);
model.ElementFactory.CreateLinearConstantStrainTriangle(node1, node2, node3, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node2, node4, node3, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node3, node4, node5, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node4, node6, node5, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, 0, -10, 0, 0, 0);
model.ApplyForceToNode(force, node3);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1); //get the reaction at the first node
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20, reaction1.Y + reaction2.Y, 0.001);
DisplacementVector displacement3 = results.GetDisplacement(node3); // get the displacement at the second node
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Assert.AreNotEqual(0.0, displacement3.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Z); // TODO calculate the actual value, rather than just checking we have any value
DisplacementVector displacement4 = results.GetDisplacement(node4); // get the displacement at the second node
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreNotEqual(0.0, displacement4.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Z); // TODO calculate the actual value, rather than just checking we have any value
}
public void Calculate2DTrussOf3BarsAnd8Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D);
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(0, 10);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(10, 10);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(10, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 30000000, 0, 0);
ICrossSection section = new SolidRectangle(2, 1);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
ForceVector externalForce = model.ForceFactory.CreateForTruss(0, -10000);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(0, reactionAtNode2.X, 1);
Assert.AreEqual(7929, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(2071, reactionAtNode3.X, 1);
Assert.AreEqual(2071, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-2071, reactionAtNode4.X, 1);
Assert.AreEqual(0, reactionAtNode4.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual( 0.00035, displacementAtNode1.X, 0.00001); ///NOTE this does not match the example in the book, but was instead verified by commercial FE software. It appears as it may be an errata in the book.
Assert.AreEqual(-0.00132, displacementAtNode1.Z, 0.00001); ///NOTE this does not match the example in the book, but was instead verified by commercial FE software. It appears as it may be an errata in the book.
}
public void AnalyzeSimple2DBuilding()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D);
//add nodes
FiniteElementNode node0 = model.NodeFactory.CreateFor2DTruss(0, 0);
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(3, 0);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(6, 0);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(9, 0);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(0, 3);
FiniteElementNode node5 = model.NodeFactory.CreateFor2DTruss(3, 3);
FiniteElementNode node6 = model.NodeFactory.CreateFor2DTruss(6, 3);
FiniteElementNode node7 = model.NodeFactory.CreateFor2DTruss(9, 3);
FiniteElementNode node8 = model.NodeFactory.CreateFor2DTruss(0, 6);
FiniteElementNode node9 = model.NodeFactory.CreateFor2DTruss(3, 6);
FiniteElementNode node10 = model.NodeFactory.CreateFor2DTruss(6, 6);
FiniteElementNode node11 = model.NodeFactory.CreateFor2DTruss(9, 6);
//add constraints
model.ConstrainNode(node0, DegreeOfFreedom.X);
model.ConstrainNode(node0, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
//properties
IMaterial material = new GenericElasticMaterial(0, 70000000, 0, 0);
ICrossSection section = new SolidRectangle(0.03, 0.01);
//add horizontal elements
LinearTruss truss0 = model.ElementFactory.CreateLinearTruss(node0, node1, material, section);
LinearTruss truss1 = model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
LinearTruss truss2 = model.ElementFactory.CreateLinearTruss(node2, node3, material, section);
LinearTruss truss3 = model.ElementFactory.CreateLinearTruss(node4, node5, material, section);
LinearTruss truss4 = model.ElementFactory.CreateLinearTruss(node5, node6, material, section);
LinearTruss truss5 = model.ElementFactory.CreateLinearTruss(node6, node7, material, section);
LinearTruss truss6 = model.ElementFactory.CreateLinearTruss(node8, node9, material, section);
LinearTruss truss7 = model.ElementFactory.CreateLinearTruss(node9, node10, material, section);
LinearTruss truss8 = model.ElementFactory.CreateLinearTruss(node10, node11, material, section);
//add vert elements
LinearTruss truss9 = model.ElementFactory.CreateLinearTruss(node0, node4, material, section);
LinearTruss truss10 = model.ElementFactory.CreateLinearTruss(node4, node8, material, section);
LinearTruss truss11 = model.ElementFactory.CreateLinearTruss(node1, node5, material, section);
LinearTruss truss12 = model.ElementFactory.CreateLinearTruss(node5, node9, material, section);
LinearTruss truss13 = model.ElementFactory.CreateLinearTruss(node2, node6, material, section);
LinearTruss truss14 = model.ElementFactory.CreateLinearTruss(node6, node10, material, section);
LinearTruss truss15 = model.ElementFactory.CreateLinearTruss(node3, node7, material, section);
LinearTruss truss16 = model.ElementFactory.CreateLinearTruss(node7, node11, material, section);
//add bracing
LinearTruss truss17 = model.ElementFactory.CreateLinearTruss(node1, node6, material, section);
LinearTruss truss18 = model.ElementFactory.CreateLinearTruss(node2, node5, material, section);
LinearTruss truss19 = model.ElementFactory.CreateLinearTruss(node5, node10, material, section);
LinearTruss truss20 = model.ElementFactory.CreateLinearTruss(node6, node9, material, section);
ForceVector force50Z = model.ForceFactory.CreateForTruss(0, 50000);
model.ApplyForceToNode(force50Z, node11);
//model.ApplyForceToNode(force50Z, node8);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
DisplacementVector displacementAtNode11 = results.GetDisplacement(node11);
double dispX = displacementAtNode11.X;
double dispY = displacementAtNode11.Y;
//Assert.AreEqual(7.1429, displacementAtNode11.X, 0.001);
//Assert.AreEqual(-9.0386, displacementAtNode11.Z, 0.001);
//FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(0, 3);
}
public void SpringAt60DegreesInXYPlane()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D); // we will create and analyze a 2D truss system
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // also constrain it from moving in the Y axis
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(1, 1.73205); // create a second node at a distance 1 metre along the X axis and 1.73 metres along the Y axis (giving an angle of 60 degrees from x-axis).
model.ConstrainNode(node2, DegreeOfFreedom.X);
LinearConstantSpring spring = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000); // create a spring between the first two nodes of a stiffness of 1000 Newtons per metre
ForceVector force = model.ForceFactory.CreateForTruss(0, 10); // Create a force of with components of 10 Newtons along the y-axis.
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0, displacementAtNode2.X); // Check that there is no displacement in the x-axis
Assert.AreEqual(0.013333, displacementAtNode2.Z, 0.001); // and 0.01333 metres (13 millimetres) along the Y axis.
ReactionVector reactionAtNode1 = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-5.774, reactionAtNode1.X, 0.001); // Check that we have calculated a reaction of 10/SQRT(3) Newtons in the X axis.
Assert.AreEqual(-10, reactionAtNode1.Z, 0.001); // and a reaction of -10 Newtons in the Y axis.
}
public void ThreeNodeBeam()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(1, 0, 0);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
FiniteElementNode node3 = model.NodeFactory.Create(2, 0, 0);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 10000000000, 0.3, 1000000000);
ICrossSection section = new SolidRectangle(1, 1);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
Stiffness.GlobalModelStiffnessMatrixBuilder gmsmb = new SharpFE.Stiffness.GlobalModelStiffnessMatrixBuilder(model);
Console.WriteLine(gmsmb.BuildKnownForcesUnknownDisplacementStiffnessMatrix());
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
Console.WriteLine("node1Displacement : \n" + node1Displacement);
DisplacementVector node2Displacement = results.GetDisplacement(node2);
Console.WriteLine("node2Displacement : \n" + node2Displacement);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
Console.WriteLine("node3Displacement : \n" + node3Displacement);
ReactionVector node1Reaction = results.GetReaction(node1);
Console.WriteLine("node1Reaction : \n" + node1Reaction);
ReactionVector node3Reaction = results.GetReaction(node3);
Console.WriteLine("node5Reaction : \n" + node3Reaction);
Assert.AreEqual(0, node2Displacement.XX, 0.00001);
Assert.AreEqual(0, node2Displacement.Y, 0.00001);
Assert.AreEqual(0, node2Displacement.ZZ, 0.0001);
Assert.AreEqual(-0.000002, node2Displacement.Z, 0.0000001);
Assert.AreEqual(5000, node1Reaction.Z, 0.00001);
Assert.AreEqual(5000, node3Reaction.Z, 0.00001);
Assert.AreEqual(0, node2Displacement.YY, 0.0001);
Assert.AreEqual(0.000003, node1Displacement.YY, 0.0000001);
Assert.AreEqual(-0.000003, node3Displacement.YY, 0.0000001);
}
public void SpringInXAxis()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D); // we will create and analyze a 1D spring in the vertical
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain this node from moving in the X axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // also constrain it from moving in the Y axis
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(1, 0); // create a second node at a distance 1 metre along the X axis.
model.ConstrainNode(node2, DegreeOfFreedom.Z); // fix this node from moving along the Y-axis. It is still free to move along the X-axis however.
LinearConstantSpring spring = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000); // create a spring between the two nodes of a stiffness of 1000 Newtons per metre
ForceVector force = model.ForceFactory.CreateForTruss(10, 0); // Create a force of 10 Newtons along the x-axis.
model.ApplyForceToNode(force, node2); // Apply that force to the second node
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model); // Create a new instance of the solver class and pass it the model to solve
FiniteElementResults results = solver.Solve(); // ask the solver to solve the model and return results
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2); // get the displacement at the second node
Assert.AreEqual(0.01, displacementAtNode2.X); // check that we calculated 0.010 metres (10 millimetres) along the Y axis.
ReactionVector reactionAtNode1 = results.GetReaction(node1); //get the reaction at the first node
Assert.AreEqual(-10, reactionAtNode1.X); // Check that we have calculated a reaction of -10 Newtons in the X axis.
Assert.AreEqual(0, reactionAtNode1.Z); // and a reaction of 0 Newtons in the Y axis.
}
public void Calculate3DPortalFrameOf8BeamsAnd48Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(0, -4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(4, -4, 0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(4, 0, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
FiniteElementNode node5 = model.NodeFactory.Create(0, 0, 5);
FiniteElementNode node6 = model.NodeFactory.Create(0, -4, 5);
FiniteElementNode node7 = model.NodeFactory.Create(4, -4, 5);
FiniteElementNode node8 = model.NodeFactory.Create(4, 0, 5);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0001, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node5, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node6, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node7, material, section);
model.ElementFactory.CreateLinear3DBeam(node4, node8, material, section);
model.ElementFactory.CreateLinear3DBeam(node5, node6, material, section);
model.ElementFactory.CreateLinear3DBeam(node6, node7, material, section);
model.ElementFactory.CreateLinear3DBeam(node7, node8, material, section);
model.ElementFactory.CreateLinear3DBeam(node8, node5, material, section);
ForceVector force = model.ForceFactory.Create(-15000, 0, 0, 0, 0, 0);
model.ApplyForceToNode(force, node7);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
DisplacementVector node5Displacement = results.GetDisplacement(node5);
DisplacementVector node6Displacement = results.GetDisplacement(node6);
DisplacementVector node7Displacement = results.GetDisplacement(node7);
DisplacementVector node8Displacement = results.GetDisplacement(node8);
// Console.WriteLine("\nNode5 displacement : \n" + node5Displacement);
// Console.WriteLine("\nNode6 displacement : \n" + node6Displacement);
// Console.WriteLine("\nNode7 displacement : \n" + node7Displacement);
// Console.WriteLine("\nNode8 displacement : \n" + node8Displacement);
Assert.Inconclusive("The below tests pass for y-displacements, but fail for x-displacements");
Assert.AreEqual(-0.0026743, node5Displacement.X, 0.0001);
Assert.AreEqual(0.0038697, node5Displacement.Y, 0.0001);
Assert.AreEqual(-0.0107708, node6Displacement.X, 0.0001);
Assert.AreEqual(0.0038697, node6Displacement.Y, 0.0001);
Assert.AreEqual(-0.0107780, node7Displacement.X, 0.0001);
Assert.AreEqual(-0.0038697, node7Displacement.Y, 0.0001);
Assert.AreEqual(-0.0026743, node8Displacement.X, 0.0001);
Assert.AreEqual(-0.0038697, node8Displacement.Y, 0.0001);
}
public void Calculate2DTrussOf11BarsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss2D);
//build geometric model and constraints
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(0, 3);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(3, 0);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(3, 3);
FiniteElementNode node5 = model.NodeFactory.CreateFor2DTruss(6, 0);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.CreateFor2DTruss(6, 3);
IMaterial material = new GenericElasticMaterial(0, 70000000, 0, 0);
ICrossSection section = new SolidRectangle(0.03, 0.01);
LinearTruss truss1 = model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
LinearTruss truss2 = model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
LinearTruss truss3 = model.ElementFactory.CreateLinearTruss(node2, node3, material, section);
LinearTruss truss4 = model.ElementFactory.CreateLinearTruss(node2, node4, material, section);
LinearTruss truss5 = model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
LinearTruss truss6 = model.ElementFactory.CreateLinearTruss(node3, node4, material, section);
LinearTruss truss7 = model.ElementFactory.CreateLinearTruss(node3, node6, material, section);
LinearTruss truss8 = model.ElementFactory.CreateLinearTruss(node4, node5, material, section);
LinearTruss truss9 = model.ElementFactory.CreateLinearTruss(node4, node6, material, section);
LinearTruss truss10 = model.ElementFactory.CreateLinearTruss(node3, node5, material, section);
LinearTruss truss11 = model.ElementFactory.CreateLinearTruss(node5, node6, material, section);
//apply forces
ForceVector force50Z = model.ForceFactory.CreateForTruss(0, -50000);
model.ApplyForceToNode(force50Z, node2);
model.ApplyForceToNode(force50Z, node6);
ForceVector force100Z = model.ForceFactory.CreateForTruss(0, -100000);
model.ApplyForceToNode(force100Z, node4);
//solve model
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
//assert results
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode1.X, 1);
Assert.AreEqual(100000, reactionAtNode1.Z, 1);
ReactionVector reactionAtNode5 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode5.X, 1);
Assert.AreEqual(100000, reactionAtNode5.Z, 1);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(7.1429, displacementAtNode2.X, 0.001);
Assert.AreEqual(-9.0386, displacementAtNode2.Z, 0.001);
DisplacementVector displacementAtNode3 = results.GetDisplacement(node3);
Assert.AreEqual(5.2471, displacementAtNode3.X, 0.001);
Assert.AreEqual(-16.2965, displacementAtNode3.Z, 0.001);
DisplacementVector displacementAtNode4 = results.GetDisplacement(node4);
Assert.AreEqual(5.2471, displacementAtNode4.X, 0.001);
Assert.AreEqual(-20.0881, displacementAtNode4.Z, 0.001);
DisplacementVector displacementAtNode5 = results.GetDisplacement(node5);
Assert.AreEqual(10.4942, displacementAtNode5.X, 0.001);
Assert.AreEqual(0, displacementAtNode5.Z, 0.001);
DisplacementVector displacementAtNode6 = results.GetDisplacement(node6);
Assert.AreEqual(3.3513, displacementAtNode6.X, 0.001);
Assert.AreEqual(-9.0386, displacementAtNode6.Z, 0.001);
}
public void PitchedRoofPortalFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(-10, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(-10, 0, 10);
FiniteElementNode node3 = model.NodeFactory.Create(0, 0, 14);
FiniteElementNode node4 = model.NodeFactory.Create(10, 0, 10);
FiniteElementNode node5 = model.NodeFactory.Create(10, 0, 0);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.XX);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node4, material, section);
model.ElementFactory.CreateLinear3DBeam(node4, node5, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, 10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
DisplacementVector node2Displacement = results.GetDisplacement(node2);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
DisplacementVector node4Displacement = results.GetDisplacement(node4);
DisplacementVector node5Displacement = results.GetDisplacement(node5);
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node5Reaction = results.GetReaction(node5);
Assert.AreEqual(0, node1Displacement.X, 0.0001);
Assert.AreEqual(0, node1Displacement.Y, 0.0001);
Assert.AreEqual(0, node1Displacement.Z, 0.0001);
Assert.AreEqual(0.0010985, node1Displacement.YY, 0.0001);
Assert.AreEqual(0.004027, node2Displacement.X, 0.0001);
Assert.AreEqual(0, node2Displacement.Y, 0.0001);
Assert.AreEqual(0.002381, node2Displacement.Z, 0.0001);
Assert.AreEqual(-0.000996, node2Displacement.YY, 0.0001);
Assert.AreEqual(0, node3Displacement.X, 0.0001);
Assert.AreEqual(0, node3Displacement.Y, 0.0001);
Assert.AreEqual(0.01723, node3Displacement.Z, 0.0001);
Assert.AreEqual(0, node3Displacement.YY, 0.0001);
Assert.AreEqual(-0.004027, node4Displacement.X, 0.0001);
Assert.AreEqual(0, node4Displacement.Y, 0.0001);
Assert.AreEqual(0.002381, node4Displacement.Z, 0.0001);
Assert.AreEqual(0.000996, node4Displacement.YY, 0.0001);
Assert.AreEqual(0, node5Displacement.X, 0.0001);
Assert.AreEqual(0, node5Displacement.Y, 0.0001);
Assert.AreEqual(0, node5Displacement.Z, 0.0001);
Assert.AreEqual(-0.0010985, node5Displacement.YY, 0.0001);
Assert.AreEqual(-5000, node1Reaction.Z, 1);
Assert.AreEqual(-1759, node1Reaction.X, 1);
Assert.AreEqual(0, node1Reaction.YY, 1);
Assert.AreEqual(-5000, node5Reaction.Z, 1);
Assert.AreEqual(1759, node5Reaction.X, 1);
Assert.AreEqual(0, node5Reaction.YY, 1);
}
public void Calculate3DTrussOf3BarsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss3D);
FiniteElementNode node1 = model.NodeFactory.Create(72,0,0);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
FiniteElementNode node2 = model.NodeFactory.Create(0, 36, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 36, 72);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(0, 0, -48);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 1200000, 0, 0);
ICrossSection section1 = new SolidRectangle(1, 0.302);
ICrossSection section2 = new SolidRectangle(1, 0.729); ///NOTE example also refers to this as A1. Assume errata in book
ICrossSection section3 = new SolidRectangle(1, 0.187); ///NOTE example also refers to this as A1. Assume errata in book
model.ElementFactory.CreateLinearTruss(node1, node2, material, section1);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section2);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section3);
ForceVector externalForce = model.ForceFactory.Create(0, 0, -1000, 0, 0, 0);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(0, reactionAtNode1.X, 1);
Assert.AreEqual(-223.1632, reactionAtNode1.Y, 1);
Assert.AreEqual(0, reactionAtNode1.Z, 1);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(256.1226, reactionAtNode2.X, 1);
Assert.AreEqual(-128.0613, reactionAtNode2.Y, 1);
Assert.AreEqual(0, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(-702.4491, reactionAtNode3.X, 1);
Assert.AreEqual(351.2245, reactionAtNode3.Y, 1);
Assert.AreEqual(702.4491, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(446.3264, reactionAtNode4.X, 1);
Assert.AreEqual(0, reactionAtNode4.Y, 1);
Assert.AreEqual(297.5509, reactionAtNode4.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(-0.0711, displacementAtNode1.X, 0.0001);
Assert.AreEqual(0, displacementAtNode1.Y, 0.0001);
Assert.AreEqual(-0.2662, displacementAtNode1.Z, 0.0001);
}
public void Calculate3DTrussOf4BarsAnd15Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss3D);
FiniteElementNode node1 = model.NodeFactory.Create(4, 4, 3);
FiniteElementNode node2 = model.NodeFactory.Create(0, 4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0, 4, 6);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(4, 0, 3);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
FiniteElementNode node5 = model.NodeFactory.Create(8, -1, 1);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new SolidRectangle(0.01, 0.01);
model.ElementFactory.CreateLinearTruss(node1, node2, material, section);
model.ElementFactory.CreateLinearTruss(node1, node3, material, section);
model.ElementFactory.CreateLinearTruss(node1, node4, material, section);
model.ElementFactory.CreateLinearTruss(node1, node5, material, section);
ForceVector externalForce = model.ForceFactory.Create(0, -10000, 0, 0, 0, 0);
model.ApplyForceToNode(externalForce, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(270.9, reactionAtNode2.X, 1);
Assert.AreEqual(0, reactionAtNode2.Y, 1);
Assert.AreEqual(203.2, reactionAtNode2.Z, 1);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(1354.6, reactionAtNode3.X, 1);
Assert.AreEqual(0, reactionAtNode3.Y, 1);
Assert.AreEqual(-1016, reactionAtNode3.Z, 1);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(0, reactionAtNode4.X, 1);
Assert.AreEqual(7968.1, reactionAtNode4.Y, 1);
Assert.AreEqual(0, reactionAtNode4.Z, 1);
ReactionVector reactionAtNode5 = results.GetReaction(node5);
Assert.AreEqual(-1625.5, reactionAtNode5.X, 1);
Assert.AreEqual(2031.9, reactionAtNode5.Y, 1);
Assert.AreEqual(812.8, reactionAtNode5.Z, 1);
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(-0.0003024, displacementAtNode1.X, 0.0001); //NOTE the results given in the book are 1E03
Assert.AreEqual(-0.0015177, displacementAtNode1.Y, 0.0001);
Assert.AreEqual(0.0002688, displacementAtNode1.Z, 0.0001);
}
public void QuadMembraneAFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(1.0, 1.0, 1.0);
FiniteElementNode node4 = model.NodeFactory.Create(0.0, 1.0, 1.0);
FiniteElementNode node5 = model.NodeFactory.Create(1.0, 2.0, 0.0);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.Create(0.0, 2.0, 0.0);
model.ConstrainNode(node6, DegreeOfFreedom.X);
model.ConstrainNode(node6, DegreeOfFreedom.Y);
model.ConstrainNode(node6, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0.3, 0);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node1, node2, node3, node4, material, 0.1);
model.ElementFactory.CreateLinearConstantStressQuadrilateral(node5, node6, node4, node3, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1);
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction5 = results.GetReaction(node5);
Console.WriteLine("\nReaction2 : \n" + reaction2);
ReactionVector reaction6 = results.GetReaction(node6);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20000, reaction1.Z + reaction2.Z + reaction5.Z + reaction6.Z, 1);
DisplacementVector displacement3 = results.GetDisplacement(node3);
DisplacementVector displacement4 = results.GetDisplacement(node4);
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreEqual(0.0000002020, displacement3.X, 0.0000000001);
Assert.AreEqual(0, displacement3.Y, 0.0000000001);
Assert.AreEqual(-0.0000013469, displacement3.Z, 0.0000000001);
Assert.AreEqual(0, displacement4.X, 0.0000000001);
Assert.AreEqual(0, displacement4.Y, 0.0000000001);
Assert.AreEqual(-0.0000013469, displacement4.Z, 0.0000000001);
}
public void PortalFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(-10, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(-10, 0, 10);
FiniteElementNode node3 = model.NodeFactory.Create(0, 0, 14);
FiniteElementNode node4 = model.NodeFactory.Create(10, 0, 10);
FiniteElementNode node5 = model.NodeFactory.Create(10, 0, 0);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
model.ConstrainNode(node5, DegreeOfFreedom.XX);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node4, material, section);
model.ElementFactory.CreateLinear3DBeam(node4, node5, material, section);
ForceVector force = model.ForceFactory.Create(0, 0, 10000, 0, 0, 0);
model.ApplyForceToNode(force, node3);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
DisplacementVector node2Displacement = results.GetDisplacement(node2);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
DisplacementVector node4Displacement = results.GetDisplacement(node4);
DisplacementVector node5Displacement = results.GetDisplacement(node5);
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node5Reaction = results.GetReaction(node5);
Assert.AreEqual(0, node1Displacement.X, 0.0001);
Assert.AreEqual(0, node1Displacement.Z, 0.0001);
Assert.AreEqual(0.0010985, node1Displacement.YY, 0.0001);
Assert.AreEqual(0.004027, node2Displacement.X, 0.0001);
Assert.AreEqual(0.002381, node2Displacement.Z, 0.0001);
Assert.AreEqual(-0.000996, node2Displacement.YY, 0.0001);
Assert.AreEqual(0, node3Displacement.X, 0.0001);
Assert.AreEqual(0.01723, node3Displacement.Z, 0.0001);
Assert.AreEqual(0, node3Displacement.YY, 0.0001);
Assert.AreEqual(-0.004027, node4Displacement.X, 0.0001);
Assert.AreEqual(0.002381, node4Displacement.Z, 0.0001);
Assert.AreEqual(0.000996, node4Displacement.YY, 0.0001);
Assert.AreEqual(0, node5Displacement.X, 0.0001);
Assert.AreEqual(0, node5Displacement.Z, 0.0001);
Assert.AreEqual(-0.0010985, node5Displacement.YY, 0.0001);
Assert.AreEqual(-1759, node1Reaction.X, 1);
Assert.AreEqual(-5000, node1Reaction.Z, 1);
Assert.AreEqual(0, node1Reaction.YY, 1);
Assert.AreEqual(1759, node5Reaction.X, 1);
Assert.AreEqual(-5000, node5Reaction.Z, 1);
Assert.AreEqual(0, node5Reaction.YY, 1);
}
private void Create2DSingleSpringModelAroundOrigin(double x, double z)
{
model = new FiniteElementModel(ModelType.Truss2D);
node1 = model.NodeFactory.CreateFor2DTruss(0, 0);
node2 = model.NodeFactory.CreateFor2DTruss(x, z);
spring1 = model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1000);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.X);
force1 = model.ForceFactory.CreateForTruss(0, -10);
model.ApplyForceToNode(force1, node2);
SUT = new LinearSolverSVD(model);
}
public void SimplySupportedBeam()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
model.ConstrainNode(node2, DegreeOfFreedom.XX);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
ForceVector moment = model.ForceFactory.Create(0, 0, 0, 0, 10000, 0);
model.ApplyForceToNode(moment, node1);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
// check the results
DisplacementVector displacementAtNode1 = results.GetDisplacement(node1);
Assert.AreEqual(0, displacementAtNode1.Z, 0.001);
Assert.AreEqual(0.00007936, displacementAtNode1.YY, 0.000001);
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(0, displacementAtNode2.Z, 0.001);
Assert.AreEqual(-0.00003968, displacementAtNode2.YY, 0.000001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-10000, reactionAtNode1.Z, 0.001);
Assert.AreEqual(0, reactionAtNode1.YY, 0.001);
ReactionVector reactionAtNode2 = results.GetReaction(node2);
Assert.AreEqual(10000, reactionAtNode2.Z, 0.001);
Assert.AreEqual(0, reactionAtNode2.YY, 0.001);
}
public void Calculate3DPortalFrameOf8BeamsAnd48Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(0, -4, 0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(4, -4, 0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
FiniteElementNode node4 = model.NodeFactory.Create(4, 0, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Y);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
FiniteElementNode node5 = model.NodeFactory.Create(0, 0, 5);
FiniteElementNode node6 = model.NodeFactory.Create(0, -4, 5);
FiniteElementNode node7 = model.NodeFactory.Create(4, -4, 5);
FiniteElementNode node8 = model.NodeFactory.Create(4, 0, 5);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.02, 0.0001, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node5, material, section);
model.ElementFactory.CreateLinear3DBeam(node2, node6, material, section);
model.ElementFactory.CreateLinear3DBeam(node3, node7, material, section);
model.ElementFactory.CreateLinear3DBeam(node4, node8, material, section);
model.ElementFactory.CreateLinear3DBeam(node5, node6, material, section);
model.ElementFactory.CreateLinear3DBeam(node6, node7, material, section);
model.ElementFactory.CreateLinear3DBeam(node7, node8, material, section);
model.ElementFactory.CreateLinear3DBeam(node8, node5, material, section);
ForceVector force = model.ForceFactory.Create(-15000, 0, 0, 0, 0, 0);
model.ApplyForceToNode(force, node7);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
ReactionVector node1Reaction = results.GetReaction(node1);
ReactionVector node2Reaction = results.GetReaction(node2);
ReactionVector node3Reaction = results.GetReaction(node3);
ReactionVector node4Reaction = results.GetReaction(node4);
DisplacementVector node5Displacement = results.GetDisplacement(node5);
DisplacementVector node6Displacement = results.GetDisplacement(node6);
DisplacementVector node7Displacement = results.GetDisplacement(node7);
DisplacementVector node8Displacement = results.GetDisplacement(node8);
// Console.WriteLine("\nNode5 displacement : \n" + node5Displacement);
// Console.WriteLine("\nNode6 displacement : \n" + node6Displacement);
// Console.WriteLine("\nNode7 displacement : \n" + node7Displacement);
// Console.WriteLine("\nNode8 displacement : \n" + node8Displacement);
Assert.Inconclusive("The below tests pass for y-displacements, but fail for x-displacements");
Assert.AreEqual(-0.0026743, node5Displacement.X, 0.0001);
Assert.AreEqual(0.0038697, node5Displacement.Y, 0.0001);
Assert.AreEqual(-0.0107708, node6Displacement.X, 0.0001);
Assert.AreEqual(0.0038697, node6Displacement.Y, 0.0001);
Assert.AreEqual(-0.0107780, node7Displacement.X, 0.0001);
Assert.AreEqual(-0.0038697, node7Displacement.Y, 0.0001);
Assert.AreEqual(-0.0026743, node8Displacement.X, 0.0001);
Assert.AreEqual(-0.0038697, node8Displacement.Y, 0.0001);
}
public void ThreeNodeSimplySupportedBeam()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Full3D);
FiniteElementNode node1 = model.NodeFactory.Create(0, 0, 0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.XX);
FiniteElementNode node2 = model.NodeFactory.Create(1, 0, 0);
FiniteElementNode node3 = model.NodeFactory.Create(2, 0, 0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
model.ConstrainNode(node3, DegreeOfFreedom.Y);
model.ConstrainNode(node3, DegreeOfFreedom.Z);
model.ConstrainNode(node3, DegreeOfFreedom.XX);
IMaterial material = new GenericElasticMaterial(0, 10000000000, 0, 84000000000);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002, 0.0002, 0.00005);
model.ElementFactory.CreateLinear3DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear3DBeam(node2,node3,material,section);
ForceVector force = model.ForceFactory.Create(0, 0, -10000, 0, 0, 0);
model.ApplyForceToNode(force, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
Stiffness.GlobalModelStiffnessMatrixBuilder gmsmb = new SharpFE.Stiffness.GlobalModelStiffnessMatrixBuilder(model);
Console.WriteLine(gmsmb.BuildKnownForcesUnknownDisplacementStiffnessMatrix());
FiniteElementResults results = solver.Solve();
DisplacementVector node1Displacement = results.GetDisplacement(node1);
Console.WriteLine("node1Displacement : " + node1Displacement);
DisplacementVector node2Displacement = results.GetDisplacement(node2);
Console.WriteLine("node2Displacement : " + node2Displacement);
DisplacementVector node3Displacement = results.GetDisplacement(node3);
Console.WriteLine("node3Displacement : " + node3Displacement);
ReactionVector node1Reaction = results.GetReaction(node1);
Console.WriteLine("node1Reaction : " + node1Reaction);
ReactionVector node3Reaction = results.GetReaction(node3);
Console.WriteLine("node5Reaction : " + node3Reaction);
Assert.AreEqual(-0.000833333, node2Displacement.Z, 0.0000001);
Assert.AreEqual(5000, node1Reaction.Z, 0.001);
Assert.AreEqual(5000, node3Reaction.Z, 0.001);
Assert.AreEqual(0, node2Displacement.YY, 0.0001);
Assert.AreEqual( 0.00125, node1Displacement.YY, 0.0000001);
Assert.AreEqual(-0.00125, node3Displacement.YY, 0.0000001);
}
public void Setup()
{
SUT = new FiniteElementModel(ModelType.Truss1D);
node1 = SUT.NodeFactory.Create(0);
node2 = SUT.NodeFactory.Create(1);
node3 = SUT.NodeFactory.Create(2);
spring1 = SUT.ElementFactory.CreateLinearConstantSpring(node1, node2, 3);
spring2 = SUT.ElementFactory.CreateLinearConstantSpring(node2, node3, 2);
SUT.ConstrainNode(node1, DegreeOfFreedom.X);
SUT.ConstrainNode(node3, DegreeOfFreedom.X);
force1 = SUT.ForceFactory.Create(20);
SUT.ApplyForceToNode(force1, node2);
}
public void CalculateModelOfThreeSpringsWithFourDegreesOfFreedom()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Truss1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
FiniteElementNode node2 = model.NodeFactory.Create(1.0);
FiniteElementNode node3 = model.NodeFactory.Create(2.0);
model.ConstrainNode(node3, DegreeOfFreedom.X);
FiniteElementNode node4 = model.NodeFactory.Create(2.00001); ///TODO allow multiple nodes to be added in the same location
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ElementFactory.CreateLinearConstantSpring(node1, node2, 1);
model.ElementFactory.CreateLinearConstantSpring(node2, node3, 1);
model.ElementFactory.CreateLinearConstantSpring(node2, node4, 1);
ForceVector externalForce = model.ForceFactory.Create(10);
model.ApplyForceToNode(externalForce, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
DisplacementVector displacementAtNode2 = results.GetDisplacement(node2);
Assert.AreEqual(3.333, displacementAtNode2.X, 0.001);
ReactionVector reactionAtNode1 = results.GetReaction(node1);
Assert.AreEqual(-3.333, reactionAtNode1.X, 0.001);
ReactionVector reactionAtNode3 = results.GetReaction(node3);
Assert.AreEqual(-3.333, reactionAtNode3.X, 0.001);
ReactionVector reactionAtNode4 = results.GetReaction(node4);
Assert.AreEqual(-3.333, reactionAtNode4.X, 0.001);
}
public void FourTriangleAFrame()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D);
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Y);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0);
model.ConstrainNode(node2, DegreeOfFreedom.X);
model.ConstrainNode(node2, DegreeOfFreedom.Y);
model.ConstrainNode(node2, DegreeOfFreedom.Z);
FiniteElementNode node3 = model.NodeFactory.Create(0.0, 1.0, 0.5);
FiniteElementNode node4 = model.NodeFactory.Create(1.0, 1.0, 0.5);
FiniteElementNode node5 = model.NodeFactory.Create(0.0, 2.0, 0.0);
model.ConstrainNode(node5, DegreeOfFreedom.X);
model.ConstrainNode(node5, DegreeOfFreedom.Y);
model.ConstrainNode(node5, DegreeOfFreedom.Z);
FiniteElementNode node6 = model.NodeFactory.Create(1.0, 2.0, 0.0);
model.ConstrainNode(node6, DegreeOfFreedom.X);
model.ConstrainNode(node6, DegreeOfFreedom.Y);
model.ConstrainNode(node6, DegreeOfFreedom.Z);
IMaterial material = new GenericElasticMaterial(0, 200000, 0.2, 84000);
model.ElementFactory.CreateLinearConstantStrainTriangle(node1, node2, node3, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node2, node4, node3, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node3, node4, node5, material, 0.1);
model.ElementFactory.CreateLinearConstantStrainTriangle(node4, node6, node5, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, 0, -10, 0, 0, 0);
model.ApplyForceToNode(force, node3);
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new LinearSolverSVD(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1); //get the reaction at the first node
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20, reaction1.Y + reaction2.Y, 0.001);
DisplacementVector displacement3 = results.GetDisplacement(node3); // get the displacement at the second node
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Assert.AreNotEqual(0.0, displacement3.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Z); // TODO calculate the actual value, rather than just checking we have any value
DisplacementVector displacement4 = results.GetDisplacement(node4); // get the displacement at the second node
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreNotEqual(0.0, displacement4.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Z); // TODO calculate the actual value, rather than just checking we have any value
}
public void TwoTriangleWall()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Membrane3D); // we will create and analyze a 2D slab system
FiniteElementNode node1 = model.NodeFactory.Create(0.0, 0.0, 0.0); // create a node at the origin
model.ConstrainNode(node1, DegreeOfFreedom.X); // constrain the node from moving in the x-axis
model.ConstrainNode(node1, DegreeOfFreedom.Y); // constrain the node from moving in the y-axis
model.ConstrainNode(node1, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node2 = model.NodeFactory.Create(1.0, 0.0, 0.0); // create a second node at a distance 1 metre along the X axis
model.ConstrainNode(node2, DegreeOfFreedom.X); // constrain the node from moving in the x-axis
model.ConstrainNode(node2, DegreeOfFreedom.Y); // constrain the node from moving in the y-axis
model.ConstrainNode(node2, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node3 = model.NodeFactory.Create(0.0, 1.0, 0.0);
model.ConstrainNode(node3, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
FiniteElementNode node4 = model.NodeFactory.Create(1.0, 1.0, 0.0);
model.ConstrainNode(node4, DegreeOfFreedom.Z); // constrain the node from moving in the z-axis
IMaterial material = new GenericElasticMaterial(0, 200000, 0.2, 84000);
model.ElementFactory.CreateLinearConstantStrainTriangle(node1, node2, node3, material, 0.1); // create a triangle of thickness of 0.1 metres
model.ElementFactory.CreateLinearConstantStrainTriangle(node2, node4, node3, material, 0.1);
ForceVector force = model.ForceFactory.Create(0, -10); // Create a force of 10 Newtons in the y direction
model.ApplyForceToNode(force, node3); // Apply that force to the third node
model.ApplyForceToNode(force, node4);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction1 = results.GetReaction(node1); //get the reaction at the first node
Console.WriteLine("\nReaction1 : \n" + reaction1);
ReactionVector reaction2 = results.GetReaction(node2);
Console.WriteLine("\nReaction2 : \n" + reaction2);
Assert.AreEqual(20, reaction1.Y + reaction2.Y, 0.001);
DisplacementVector displacement3 = results.GetDisplacement(node3); // get the displacement at the second node
Console.WriteLine("\nDisplacement3 : \n" + displacement3);
Assert.AreNotEqual(0.0, displacement3.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement3.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreEqual(0.0, displacement3.Z); // TODO calculate the actual value, rather than just checking we have any value
DisplacementVector displacement4 = results.GetDisplacement(node4); // get the displacement at the second node
Console.WriteLine("\nDisplacement4 : \n" + displacement4);
Assert.AreNotEqual(0.0, displacement4.X); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreNotEqual(0.0, displacement4.Y); // TODO calculate the actual value, rather than just checking we have any value
Assert.AreEqual(0.0, displacement4.Z); // TODO calculate the actual value, rather than just checking we have any value
}
public void ReversedCantilever()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Beam1D);
FiniteElementNode node1 = model.NodeFactory.Create(0);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.Create(3.0);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear1DBeam(node2, node1, material, section); //connecting the nodes in reverse order to the Cantilever() example
ForceVector force = model.ForceFactory.CreateFor1DBeam(-10000, 0);
model.ApplyForceToNode(force, node2);
IFiniteElementSolver solver = new MatrixInversionLinearSolver(model);
FiniteElementResults results = solver.Solve();
ReactionVector reaction = results.GetReaction(node1);
Assert.AreEqual(10000, reaction.Z, 0.001);
Assert.AreEqual(-30000, reaction.YY, 0.001);
DisplacementVector displacement = results.GetDisplacement(node2);
Assert.AreEqual(-0.00214, displacement.Z, 0.0005);
Assert.AreEqual(0.00107, displacement.YY, 0.0001);
}