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 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 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 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 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 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 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 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 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);
}
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 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 override ICrossSection ToSharpCrossSection()
{
GenericCrossSection crossSection = new GenericCrossSection(this.Area, this.Iyy);
return(crossSection);
}
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 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 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 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 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 Calculate2DFrameOf3BeamsAnd12Dof()
{
FiniteElementModel model = new FiniteElementModel(ModelType.Frame2D);
FiniteElementNode node1 = model.NodeFactory.CreateFor2DTruss(0, 3);
model.ConstrainNode(node1, DegreeOfFreedom.X);
model.ConstrainNode(node1, DegreeOfFreedom.Z);
model.ConstrainNode(node1, DegreeOfFreedom.YY);
FiniteElementNode node2 = model.NodeFactory.CreateFor2DTruss(3, 3);
FiniteElementNode node3 = model.NodeFactory.CreateFor2DTruss(6, 0);
FiniteElementNode node4 = model.NodeFactory.CreateFor2DTruss(9, 0);
model.ConstrainNode(node4, DegreeOfFreedom.X);
model.ConstrainNode(node4, DegreeOfFreedom.Z);
model.ConstrainNode(node4, DegreeOfFreedom.YY);
IMaterial material = new GenericElasticMaterial(0, 210000000000, 0, 0);
ICrossSection section = new GenericCrossSection(0.0001, 0.0002);
model.ElementFactory.CreateLinear1DBeam(node1, node2, material, section);
model.ElementFactory.CreateLinear1DBeam(node2, node3, material, section);
model.ElementFactory.CreateLinear1DBeam(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
Console.WriteLine(node4Reaction);
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 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 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 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 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);
}
