public double ComputeStress(List <double> elemDisplacements)
{
LinearAlgebra.Vector <double> elemDispVector = LinearAlgebra.Vector <double> .Build.Dense(elemDisplacements.ToArray());
double N = StiffnessModulus * Area / ElemLength * LinearAlgebra.Vector <double> .Build.Dense(new double[] { -1, 1 }).DotProduct(G.Multiply(elemDispVector));
return(N / Area);
}
public LinearAlgebra.Vector <double> solveEquations(LinearAlgebra.Matrix <double> stiffnessMatrix, LinearAlgebra.Vector <double> forceVector, List <int> boundaryDofs, List <double> boundaryConstraints)
{
int nDof = forceVector.Count;
// Find all dofs where force is known
List <int> allDofs = Enumerable.Range(0, nDof).ToList();
List <int> unknownDofs = allDofs.Except(boundaryDofs).ToList();
// Add the know displacements to the result
LinearAlgebra.Vector <double> displacementVector = LinearAlgebra.Vector <double> .Build.Dense(nDof);
for (int i = 0; i < boundaryDofs.Count; i++)
{
displacementVector[boundaryDofs[i]] = boundaryConstraints[i];
}
// Pick out part of matrix corresponding to known forces
int nrUnknownDofs = unknownDofs.Count;
LinearAlgebra.Matrix <double> unknownK = LinearAlgebra.Matrix <double> .Build.Dense(nrUnknownDofs, nrUnknownDofs);
LinearAlgebra.Vector <double> knownForces = LinearAlgebra.Vector <double> .Build.Dense(unknownDofs.Count);
for (int i = 0; i < unknownDofs.Count; i++)
{
for (int j = 0; j < unknownDofs.Count; j++)
{
unknownK[i, j] = stiffnessMatrix[unknownDofs[i], unknownDofs[j]];
}
knownForces[i] = forceVector[unknownDofs[i]];
}
LinearAlgebra.Matrix <double> unkownKnownK = LinearAlgebra.Matrix <double> .Build.Dense(nrUnknownDofs, boundaryDofs.Count);
for (int i = 0; i < unknownDofs.Count; i++)
{
for (int j = 0; j < boundaryDofs.Count; j++)
{
unkownKnownK[i, j] = stiffnessMatrix[unknownDofs[i], boundaryDofs[j]];
}
knownForces[i] = forceVector[unknownDofs[i]];
}
// Solve for the unknown displacements
LinearAlgebra.Vector <double> unknownDisplacements = unknownK.Inverse().Multiply(knownForces.Subtract(unkownKnownK.Multiply(LinearAlgebra.Vector <double> .Build.Dense(boundaryConstraints.ToArray()))));
// Insert the calculated displacements
for (int i = 0; i < unknownDofs.Count; i++)
{
displacementVector[unknownDofs[i]] = unknownDisplacements[i];
}
return(displacementVector);
}
/// <summary>
/// 回傳數列中最明顯的 Change Point。
/// </summary>
/// <param name="d">The numeric array which use to run change point procedure. Missing value (1.23456E+30) element is not allow in the array.</param>
/// <param name="conf">The confidence level used to test whether it is a significant change point</param>
/// <param name="N">Number of boostrap</param>
/// <returns></returns>
public static ChangePointInfo ChangePointOnSingleCase(double[] d, double conf = 0.9, int N = 1000)
{
if (d.Length < 7)
{
return new ChangePointInfo()
{
Index = -1
}
}
;
if (d.Any(x => x >= MtbTools.MISSINGVALUE))
{
throw new ArgumentException("數列中包含遺失值");
}
LinearAlgebra.Vector <double> xs = LinearAlgebra.Vector <double> .Build.DenseOfArray(d);
double xbar = xs.Average();
xs = xs - xbar; //Xi-Xbar
LinearAlgebra.Vector <double> si
= LinearAlgebra.Vector <double> .Build.DenseOfArray(MathTool.PartialSum(xs.ToArray()));
int changepointindex = si.AbsoluteMaximumIndex();
double sdiff = si.Maximum() - si.Minimum();
double[] Sdiff_boostrap = new double[N];
for (int i = 0; i < N; i++)
{
double[] si_boostrap = MathTool.PartialSum(MathTool.RandomSample(xs.ToArray()).Cast <double>().ToArray());
Sdiff_boostrap[i] = si_boostrap.Max() - si_boostrap.Min();
}
double confLv = (double)Sdiff_boostrap.Where(x => x < sdiff).Count() / N;
if (confLv < conf)
{
return new ChangePointInfo()
{
Index = -1
}
}
; //Not significant
return(new ChangePointInfo()
{
Index = changepointindex, Sdiff = sdiff, ConfidenceLevel = confLv
});
}
/// <summary>
/// 計算數列各元素的累積和
/// </summary>
/// <param name="x">要處理的陣列，合法的輸入是 double[]</param>
/// <returns></returns>
public static double[] PartialSum(double[] x)
{
LinearAlgebra.Vector <double> vx
= LinearAlgebra.Double.DenseVector.OfArray(x);
int row = vx.Count;
int col = row;
LinearAlgebra.Matrix <double> lmat
= LinearAlgebra.Matrix <double> .Build.Dense(row, col, 1);
lmat = lmat.LowerTriangle();
LinearAlgebra.Vector <double> result
= lmat.Multiply(vx);
return(result.ToArray());
}
protected override void SolveInstance(IGH_DataAccess DA)
{
// Retrive data from component
List <double> A = new List <double>();
List <double> E = new List <double>();
List <Line> lines = new List <Line>();
List <ContstraintNode> rNodes = new List <ContstraintNode>();
List <LoadNode> loadNodes = new List <LoadNode>();
double scaleFactor = 1.0;
DA.GetDataList("Line", lines);
DA.GetDataList("Area", A);
DA.GetDataList("Youngs Modulus", E);
DA.GetDataList("Restraint Nodes", rNodes);
DA.GetDataList("Load Nodes", loadNodes);
DA.GetData("Scale Factor", ref scaleFactor);
// The length of A and E must be the same as lines
if ((A.Count != E.Count) | (E.Count != lines.Count))
{
throw new ArgumentException("Length of A and E must equal length of Line");
}
// Create one list to store the nodes and one list to store the bars
List <Node> trussNodes = new List <Node>();
List <Bar> trussBars = new List <Bar>();
// Topology matrix to keep track of element dofs
List <List <int> > eDof = new List <List <int> >();
// Loop trough each line and create nodes at end points
for (int i = 0; i < lines.Count; i++)
{
Node node1 = new Node(lines[i].From);
Node node2 = new Node(lines[i].To);
// To keep track if the node is unique
bool unique1 = true;
bool unique2 = true;
// Check if node is unique, if so give it an ID and degress of freedom
foreach (Node existingNode in trussNodes)
{
// If not unique use an already identified node
if (node1 == existingNode)
{
node1 = existingNode;
unique1 = false;
}
if (node2 == existingNode)
{
node2 = existingNode;
unique2 = false;
}
}
// If unique give it an ID
if (unique1)
{
int id_node_1 = trussNodes.Count;
node1.ID = id_node_1;
node1.Dofs = System.Linq.Enumerable.Range(id_node_1 * 3, 3).ToList();
// Check if any boundary node or load node exist at current node
foreach (ContstraintNode rNode in rNodes)
{
if (rNode == node1)
{
// Add restraint data
node1.ConstraintX = rNode.ConstraintX;
node1.ConstraintY = rNode.ConstraintY;
node1.ConstraintZ = rNode.ConstraintZ;
}
}
foreach (LoadNode loadNode in loadNodes)
{
if (loadNode == node1)
{
// Add force data
node1.ForceX = loadNode.ForceX;
node1.ForceY = loadNode.ForceY;
node1.ForceZ = loadNode.ForceZ;
}
}
// Finally add the node
trussNodes.Add(node1);
}
if (unique2)
{
int id_node_2 = trussNodes.Count;
node2.ID = id_node_2;
node2.Dofs = System.Linq.Enumerable.Range(id_node_2 * 3, 3).ToList();
// Check if any boundary node or load node exist at current node
foreach (ContstraintNode rNode in rNodes)
{
if (rNode == node2)
{
// Add constraint data
node2.ConstraintX = rNode.ConstraintX;
node2.ConstraintY = rNode.ConstraintY;
node2.ConstraintZ = rNode.ConstraintZ;
}
}
foreach (LoadNode loadNode in loadNodes)
{
if (loadNode == node2)
{
// Add force data
node2.ForceX = loadNode.ForceX;
node2.ForceY = loadNode.ForceY;
node2.ForceZ = loadNode.ForceZ;
}
}
// Finally add the node
trussNodes.Add(node2);
}
// Create a bar object between the nodes
Bar bar = new Bar(node1, node2, A[i], E[i]);
trussBars.Add(bar);
// Topology matrix
List <int> dofs1 = bar.Nodes[0].Dofs;
List <int> dofs2 = bar.Nodes[1].Dofs;
List <int> eDofRow = new List <int>();
eDofRow.AddRange(dofs1);
eDofRow.AddRange(dofs2);
eDof.Add(eDofRow);
}
int nDof = trussNodes.Count * 3;
int nElem = eDof.Count;
// Loop trough each node and construct a load vector and boundary vector
LinearAlgebra.Vector <double> forceVector = LinearAlgebra.Vector <double> .Build.Dense(nDof);
List <int> boundaryDofs = new List <int>();
List <double?> boundaryConstraints = new List <double?>();
for (int i = 0; i < trussNodes.Count; i++)
{
// Load vector
forceVector[i * 3] = trussNodes[i].ForceX;
forceVector[i * 3 + 1] = trussNodes[i].ForceY;
forceVector[i * 3 + 2] = trussNodes[i].ForceZ;
// Boundary vector
for (int j = 0; j < 3; j++)
{
if (j == 0 && trussNodes[i].ConstraintX != null)
{
boundaryDofs.Add(trussNodes[i].Dofs[j]);
boundaryConstraints.Add(trussNodes[i].ConstraintX);
}
else if (j == 1 && trussNodes[i].ConstraintY != null)
{
boundaryDofs.Add(trussNodes[i].Dofs[j]);
boundaryConstraints.Add(trussNodes[i].ConstraintY);
}
else if (j == 2 && trussNodes[i].ConstraintZ != null)
{
boundaryDofs.Add(trussNodes[i].Dofs[j]);
boundaryConstraints.Add(trussNodes[i].ConstraintZ);
}
}
}
// Loop trough each element, compute local stiffness matrix and assemble into global stiffness matrix
LinearAlgebra.Matrix <double> K = LinearAlgebra.Matrix <double> .Build.Dense(nDof, nDof);
for (int i = 0; i < trussBars.Count; i++)
{
LinearAlgebra.Matrix <double> KElem = trussBars[i].ComputeStiffnessMatrix();
// Assemble
for (int k = 0; k < 6; k++)
{
for (int l = 0; l < 6; l++)
{
K[eDof[i][k], eDof[i][l]] = K[eDof[i][k], eDof[i][l]] + KElem[k, l];
}
}
}
// Calculate the displacements
Solver solver = new Solver();
LinearAlgebra.Vector <double> displacements = solver.solveEquations(K, forceVector, boundaryDofs, boundaryConstraints.Cast <double>().ToList());
// Save the displacement for each node and calculate the stress in each bar
List <double> elemStress = new List <double> {
};
for (int i = 0; i < nElem; i++)
{
double disp1 = displacements[eDof[i][0]];
double disp2 = displacements[eDof[i][1]];
double disp3 = displacements[eDof[i][2]];
double disp4 = displacements[eDof[i][3]];
double disp5 = displacements[eDof[i][4]];
double disp6 = displacements[eDof[i][5]];
Point3d newPoint1 = new Point3d(disp1 * scaleFactor, disp2 * scaleFactor, disp3 * scaleFactor);
Point3d newPoint2 = new Point3d(disp4 * scaleFactor, disp5 * scaleFactor, disp6 * scaleFactor);
// Translate original points
trussBars[i].Nodes[0].Point = trussBars[i].Nodes[0].Point + newPoint1;
trussBars[i].Nodes[1].Point = trussBars[i].Nodes[1].Point + newPoint2;
// Calculate element stress
elemStress.Add(trussBars[i].ComputeStress(new List <double> {
disp1, disp2, disp3, disp4, disp5, disp6
}));
}
// Return the deformed lines
List <Line> deformedLines = new List <Line>();
foreach (Bar bar in trussBars)
{
deformedLines.Add(new Line(bar.Nodes[0].Point, bar.Nodes[1].Point));
}
DA.SetDataList("Deformed Truss", deformedLines);
DA.SetDataList("Element Stress", elemStress);
}