/// <summary>
///
/// </summary>
/// <returns></returns>
public override StiffnessMatrix LocalStiffnessMatrix()
{
double stiffness = this.CalculateStiffnessConstant();
StiffnessMatrix matrix = new StiffnessMatrix(this.Element.SupportedLocalNodalDegreeOfFreedoms);
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, stiffness);
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, -stiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, -stiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, stiffness);
return(matrix);
}
/// <summary>
/// Returns a submatrix of the stiffness matrix.
/// </summary>
/// <param name="nodeRowKey">The rows of the returned matrix relate to <see cref="NodalDegreeOfFreedom">NodalDegreeOfFreedoms</see>, where the Node property of these NodalDegreeOfFreedom equals the nodeRowKey</param>
/// <param name="nodeColumnKey">the node which defines the columns of the submatrix</param>
/// <returns>A submatrix of the stiffness matrix</returns>
public StiffnessMatrix SubMatrix(FiniteElementNode nodeRowKey, FiniteElementNode nodeColumnKey)
{
// TODO guard against bad parameters
IList <NodalDegreeOfFreedom> validRowKeys = this.GetAllRowKeysWithMatchingNode(nodeRowKey);
IList <NodalDegreeOfFreedom> validColumnKeys = this.GetAllColumnKeysWithMatchingNode(nodeColumnKey);
StiffnessMatrix result = new StiffnessMatrix(validRowKeys, validColumnKeys);
foreach (NodalDegreeOfFreedom rowKey in validRowKeys)
{
foreach (NodalDegreeOfFreedom columnKey in validColumnKeys)
{
result.At(rowKey, columnKey, this.At(rowKey, columnKey));
}
}
return(result);
}
/// <summary>
/// This function iterates through all the elements which provide stiffnesses for the given combination of nodal degree of freedoms
/// and sums them to provide the total stiffness
/// </summary>
/// <param name="rowKeys">The nodal degree of freedoms which represent the rows of the matrix</param>
/// <param name="columnKeys">The nodal degree of freedoms which represents the columns of the matrix</param>
/// <returns>A matrix representing the stiffness for these combinations of rows and columns</returns>
private StiffnessMatrix BuildStiffnessSubMatrix(IList <NodalDegreeOfFreedom> rowKeys, IList <NodalDegreeOfFreedom> columnKeys)
{
Guard.AgainstNullArgument(rowKeys, "rowKeys");
Guard.AgainstNullArgument(columnKeys, "columnKeys");
int numRows = rowKeys.Count;
int numCols = columnKeys.Count;
Guard.AgainstBadArgument(
"rowKeys",
() => { return(numRows == 0); },
"There must be at least one row");
Guard.AgainstBadArgument(
"columnKeys",
() => { return(numCols == 0); },
"There must be at least one column");
StiffnessMatrix result = new StiffnessMatrix(rowKeys, columnKeys);
IList <IFiniteElement> connectedElements;
foreach (NodalDegreeOfFreedom row in rowKeys)
{
foreach (NodalDegreeOfFreedom column in columnKeys)
{
connectedElements = this.parent.AllElementsDirectlyConnecting(row.Node, column.Node);
double currentResult = this.SumStiffnessesForAllElementsAt(connectedElements, row, column);
if (!currentResult.IsApproximatelyEqualTo(0.0))
{
result.At(row, column, currentResult);
}
}
}
return(result);
}
/// <summary>
///
/// </summary>
/// <returns></returns>
public override StiffnessMatrix LocalStiffnessMatrix()
{
double length = this.Element.OriginalLength;
StiffnessMatrix matrix = new StiffnessMatrix(this.Element.SupportedLocalNodalDegreeOfFreedoms);
double axialStiffness = this.Element.StiffnessEA / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, axialStiffness);
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, -axialStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, -axialStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, axialStiffness);
double shearStiffnessInZ = 12.0 * this.Element.BendingStiffnessEIy / (length * length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.Z, shearStiffnessInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.Z, -shearStiffnessInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.Z, -shearStiffnessInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.Z, shearStiffnessInZ);
double bendingStiffnessAboutYY = 2.0 * this.Element.BendingStiffnessEIy / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.YY, 2.0 * bendingStiffnessAboutYY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.YY, bendingStiffnessAboutYY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.YY, bendingStiffnessAboutYY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.YY, 2.0 * bendingStiffnessAboutYY);
double bendingAboutYYShearInZ = 6.0 * this.Element.BendingStiffnessEIy / (length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.YY, -bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.YY, -bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.YY, bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.YY, bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.Z, -bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.Z, bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.Z, -bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.Z, bendingAboutYYShearInZ);
return(matrix);
}
/// <summary>
///
/// </summary>
/// <returns></returns>
public override StiffnessMatrix LocalStiffnessMatrix()
{
double length = this.Element.OriginalLength;
StiffnessMatrix matrix = new StiffnessMatrix(this.Element.SupportedLocalNodalDegreeOfFreedoms);
double axialStiffness = this.Element.CrossSection.Area * this.Element.Material.YoungsModulus / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, axialStiffness);
matrix.At(this.Element.StartNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, -axialStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.StartNode, DegreeOfFreedom.X, -axialStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.X, this.Element.EndNode, DegreeOfFreedom.X, axialStiffness);
double shearStiffnessInY = 12.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundZZ / (length * length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Y, this.Element.StartNode, DegreeOfFreedom.Y, shearStiffnessInY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Y, this.Element.EndNode, DegreeOfFreedom.Y, -shearStiffnessInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Y, this.Element.StartNode, DegreeOfFreedom.Y, -shearStiffnessInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Y, this.Element.EndNode, DegreeOfFreedom.Y, shearStiffnessInY);
double shearStiffnessInZ = 12.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundYY / (length * length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.Z, shearStiffnessInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.Z, -shearStiffnessInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.Z, -shearStiffnessInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.Z, shearStiffnessInZ);
double torsionalStiffness = this.Element.Material.ShearModulusElasticity * this.Element.CrossSection.MomentOfInertiaInTorsion / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.XX, this.Element.StartNode, DegreeOfFreedom.XX, torsionalStiffness);
matrix.At(this.Element.StartNode, DegreeOfFreedom.XX, this.Element.EndNode, DegreeOfFreedom.XX, -torsionalStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.XX, this.Element.StartNode, DegreeOfFreedom.XX, -torsionalStiffness);
matrix.At(this.Element.EndNode, DegreeOfFreedom.XX, this.Element.EndNode, DegreeOfFreedom.XX, torsionalStiffness);
double bendingStiffnessAboutYY = 2.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundYY / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.YY, 2.0 * bendingStiffnessAboutYY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.YY, bendingStiffnessAboutYY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.YY, bendingStiffnessAboutYY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.YY, 2.0 * bendingStiffnessAboutYY);
double bendingStiffnessAboutZZ = 2.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundZZ / length;
matrix.At(this.Element.StartNode, DegreeOfFreedom.ZZ, this.Element.StartNode, DegreeOfFreedom.ZZ, 2.0 * bendingStiffnessAboutZZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.ZZ, this.Element.EndNode, DegreeOfFreedom.ZZ, bendingStiffnessAboutZZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.ZZ, this.Element.StartNode, DegreeOfFreedom.ZZ, bendingStiffnessAboutZZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.ZZ, this.Element.EndNode, DegreeOfFreedom.ZZ, 2.0 * bendingStiffnessAboutZZ);
double bendingAboutZZshearInY = 6.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundZZ / (length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Y, this.Element.StartNode, DegreeOfFreedom.ZZ, bendingAboutZZshearInY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Y, this.Element.EndNode, DegreeOfFreedom.ZZ, bendingAboutZZshearInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Y, this.Element.StartNode, DegreeOfFreedom.ZZ, -bendingAboutZZshearInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Y, this.Element.EndNode, DegreeOfFreedom.ZZ, -bendingAboutZZshearInY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.ZZ, this.Element.StartNode, DegreeOfFreedom.Y, bendingAboutZZshearInY);
matrix.At(this.Element.StartNode, DegreeOfFreedom.ZZ, this.Element.EndNode, DegreeOfFreedom.Y, -bendingAboutZZshearInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.ZZ, this.Element.StartNode, DegreeOfFreedom.Y, bendingAboutZZshearInY);
matrix.At(this.Element.EndNode, DegreeOfFreedom.ZZ, this.Element.EndNode, DegreeOfFreedom.Y, -bendingAboutZZshearInY);
double bendingAboutYYShearInZ = 6.0 * this.Element.Material.YoungsModulus * this.Element.CrossSection.SecondMomentOfAreaAroundYY / (length * length);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.YY, -bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.YY, -bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.StartNode, DegreeOfFreedom.YY, bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.Z, this.Element.EndNode, DegreeOfFreedom.YY, bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.Z, -bendingAboutYYShearInZ);
matrix.At(this.Element.StartNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.Z, bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.StartNode, DegreeOfFreedom.Z, -bendingAboutYYShearInZ);
matrix.At(this.Element.EndNode, DegreeOfFreedom.YY, this.Element.EndNode, DegreeOfFreedom.Z, bendingAboutYYShearInZ);
return(matrix);
}