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 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 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 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 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 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 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.
}