Example 3: Beam3D Quaternion Nonlinear Example

The present test demonstrates the geometrically nonlinear beahvior of 3-D corotational beam portal frame structure and can be found in Beam3DQuaternionNonlinearTest.PlaneFrameTest(). The plane frame structure consists of three (3) elements and four (4) nodes.

Define the mechanical properties, nodal loads, number of nodes, number of elements and monitor node:

double youngModulus = 21000.0;
double poissonRatio = 0.3;
double nodalLoad = 500000.0;
double area = 91.04;
double inertiaY = 2843.0;
double inertiaZ = 8091.0;
double torsionalInertia = 76.57;
double effectiveAreaY = 91.04;
double effectiveAreaZ = 91.04;
int nNodes = 4;
int nElems = 3;
int monitorNode = 2;

Generate nodal geometry:

// Node creation
IList<Node> nodes = new List<Node>();
Node node1 = new Node(id: 1, x: 0.0, y: 0.0, z: 0.0);
Node node2 = new Node(id: 2, x: 0.0, y: 100.0, z: 0.0);
Node node3 = new Node(id: 3, x: 100.0, y: 100.0, z: 0.0);
Node node4 = new Node(id: 4, x: 100.0, y: 0.0, z: 0.0);

nodes.Add(node1);
nodes.Add(node2);
nodes.Add(node3);
nodes.Add(node4);

Define the model and the subdomain:

// Model creation
Model model = new Model();

// Add a single subdomain to the model
model.SubdomainsDictionary.Add(1, new Subdomain(1));

// Add nodes to the nodes dictionary of the model
for (int i = 0; i < nodes.Count; ++i)
{
	model.NodesDictionary.Add(i + 1, nodes[i]);
}

Constrain the first and the last nodes:

// Constrain first and last nodes of the model
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationX });
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationY });
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationZ });
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.RotationX });
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.RotationY });
model.NodesDictionary[1].Constraints.Add(new Constraint { DOF = StructuralDof.RotationZ });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationX });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationY });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.TranslationZ });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.RotationX });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.RotationY });
model.NodesDictionary[4].Constraints.Add(new Constraint { DOF = StructuralDof.RotationZ });

Generate the elements of the structure:

// Generate elements of the structure
int iNode = 1;
for (int iElem = 0; iElem < nElems; iElem++)
{
	// element nodes
	IList<Node> elementNodes = new List<Node>();
	elementNodes.Add(model.NodesDictionary[iNode]);
	elementNodes.Add(model.NodesDictionary[iNode + 1]);

	// Create new Beam3D section and element
	var beamSection = new BeamSection3D(area, inertiaY, inertiaZ, torsionalInertia, effectiveAreaY, effectiveAreaZ);
	var beam = new Beam3DCorotationalQuaternion(elementNodes, material, 7.85, beamSection);

	// Create elements
	var element = new Element()
	{
		ID = iElem + 1,
		ElementType = beam
	};

	var a = beam.StiffnessMatrix(element);

	// Add nodes to the created element
	element.AddNode(model.NodesDictionary[iNode]);
	element.AddNode(model.NodesDictionary[iNode + 1]);

	// Add beam element to the element and subdomains dictionary of the model
	model.ElementsDictionary.Add(element.ID, element);
	model.SubdomainsDictionary[1].Elements.Add(element);
	iNode++;
}

Loading conditions:

// Add nodal load values at the top nodes of the model
model.Loads.Add(new Load() { Amount = nodalLoad, Node = model.NodesDictionary[monitorNode], DOF = StructuralDof.TranslationX });

Define Skyline solver, Structural provider, Load Control (i.e Newton-Raphson) chlid analyzer and Static parent analyzer:

// Solver
var solverBuilder = new SkylineSolver.Builder();
ISolver solver = solverBuilder.BuildSolver(model);

// Problem type
var provider = new ProblemStructural(model, solver);

// Analyzers
int increments = 10;
var childAnalyzerBuilder = new LoadControlAnalyzer.Builder(model, solver, provider, increments);
childAnalyzerBuilder.ResidualTolerance = 1E-3;
//childAnalyzerBuilder.SubdomainUpdaters = new[] { new NonLinearSubdomainUpdater(model.SubdomainsDictionary[subdomainID]) }; // This is the default
LoadControlAnalyzer childAnalyzer = childAnalyzerBuilder.Build();
var parentAnalyzer = new StaticAnalyzer(model, solver, provider, childAnalyzer);

Output request and run the analysis:

// Request output
childAnalyzer.LogFactories[1] = new LinearAnalyzerLogFactory(new int[] { 0 });

parentAnalyzer.Initialize();
parentAnalyzer.Solve();