2-noded, linear, C0 continuous line element in 2D space. More...
#include <itkFEMElement2DC0LinearLine.h>
Public Types | |
enum | { DefaultIntegrationOrder = 1 } |
enum | { InvalidDegreeOfFreedomID = 0xffffffff } |
enum | { gaussMaxOrder = 10 } |
enum | |
enum | |
enum | |
typedef FEMPArray< Element > | ArrayType |
typedef Self | Baseclass |
typedef const Self * | ConstPointer |
typedef Superclass::DegreeOfFreedomIDType | DegreeOfFreedomIDType |
typedef Superclass::Float | Float |
typedef Superclass::LoadPointer | LoadPointer |
typedef Superclass::LoadType | LoadType |
typedef Superclass::MatrixType | MatrixType |
typedef Superclass::Node | Node |
typedef Superclass::NodeIDType | NodeIDType |
typedef Self * | Pointer |
typedef Element2DC0LinearLine | Self |
typedef TemplatedParentClass | Superclass |
typedef Superclass::VectorType | VectorType |
Public Member Functions | |
virtual int | ClassID () const =0 |
virtual Baseclass::Pointer | Clone () const =0 |
virtual Float | GetElementDeformationEnergy (MatrixType &LocalSolution) const |
virtual VectorType | GetGlobalFromLocalCoordinates (const VectorType &pt) const |
virtual void | GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order) const |
virtual void | GetLandmarkContributionMatrix (float eta, MatrixType &Le) const |
virtual void | GetLoadVector (LoadPointer l, VectorType &Fe) const =0 |
virtual bool | GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const |
virtual void | GetMassMatrix (MatrixType &Me) const |
virtual Material::ConstPointer | GetMaterial (void) const |
virtual void | GetMaterialMatrix (MatrixType &D) const =0 |
virtual NodeIDType | GetNode (unsigned int n) const |
virtual const VectorType & | GetNodeCoordinates (unsigned int n) const |
virtual unsigned int | GetNumberOfDegreesOfFreedom (void) const |
virtual unsigned int | GetNumberOfDegreesOfFreedomPerNode (void) const =0 |
virtual unsigned int | GetNumberOfIntegrationPoints (unsigned int order) const |
virtual unsigned int | GetNumberOfNodes (void) const |
virtual unsigned int | GetNumberOfSpatialDimensions () const |
virtual void | GetStiffnessMatrix (MatrixType &Ke) const |
virtual void | GetStrainDisplacementMatrix (MatrixType &B, const MatrixType &shapeDgl) const =0 |
virtual VectorType | GetStrainsAtPoint (const VectorType &pt, const Solution &sol, unsigned int index) const |
virtual VectorType | GetStressesAtPoint (const VectorType &pt, const VectorType &e, const Solution &sol, unsigned int index) const |
virtual VectorType | InterpolateSolution (const VectorType &pt, const Solution &sol, unsigned int solutionIndex=0) const |
virtual Float | InterpolateSolutionN (const VectorType &pt, const Solution &sol, unsigned int f, unsigned int solutionIndex=0) const |
virtual void | Jacobian (const VectorType &pt, MatrixType &J, const MatrixType *pshapeD=0) const |
virtual Float | JacobianDeterminant (const VectorType &pt, const MatrixType *pJ=0) const |
virtual void | JacobianInverse (const VectorType &pt, MatrixType &invJ, const MatrixType *pJ=0) const |
virtual void | Read (std::istream &, void *info) |
virtual void | SetMaterial (Material::ConstPointer) |
virtual void | SetNode (unsigned int n, NodeIDType node) |
virtual void | ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const |
virtual void | ShapeFunctionGlobalDerivatives (const VectorType &pt, MatrixType &shapeDgl, const MatrixType *pJ=0, const MatrixType *pshapeD=0) const |
virtual VectorType | ShapeFunctions (const VectorType &pt) const |
virtual void | Write (std::ostream &f) const |
DegreeOfFreedomIDType | GetDegreeOfFreedom (unsigned int local_dof) const |
Static Public Member Functions | |
static FEMLightObject::Pointer | CreateFromStream (std::istream &f, void *info) |
static void | SkipWhiteSpace (std::istream &f) |
Public Attributes | |
int | GN |
Static Public Attributes | |
static const Float | gaussPoint [gaussMaxOrder+1][gaussMaxOrder] |
static const Float | gaussWeight [gaussMaxOrder+1][gaussMaxOrder] |
static const std::string | whitespaces |
Protected Attributes | |
NodeIDType | m_node [NumberOfNodes] |
2-noded, linear, C0 continuous line element in 2D space.
Definition at line 30 of file itkFEMElement2DC0LinearLine.h.
typedef FEMPArray<Element> itk::fem::Element::ArrayType [inherited] |
Array class that holds special pointers to the Element objects
Definition at line 88 of file itkFEMElementBase.h.
typedef Self itk::fem::FEMLightObject::Baseclass [inherited] |
Store the base class typedef for easy access from derived classes. FEM_CLASS macro also expects this for the FEMOF...
Definition at line 64 of file itkFEMLightObject.h.
typedef const Self* itk::fem::Element2DC0LinearLine::ConstPointer |
Const pointer or SmartPointer to an object.
Reimplemented from itk::fem::ElementStd< 2, 2 >.
Reimplemented in itk::fem::Element2DC0LinearLineStress, and itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 33 of file itkFEMElement2DC0LinearLine.h.
typedef Superclass::DegreeOfFreedomIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::DegreeOfFreedomIDType [inherited] |
Reimplemented from itk::fem::Element.
Definition at line 67 of file itkFEMElementStd.h.
typedef Superclass::Float itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::Float [inherited] |
Reimplemented from itk::fem::Element.
Reimplemented in itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 61 of file itkFEMElementStd.h.
typedef Superclass::LoadPointer itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::LoadPointer [inherited] |
Reimplemented from itk::fem::Element.
Definition at line 65 of file itkFEMElementStd.h.
typedef Superclass::LoadType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::LoadType [inherited] |
Reimplemented from itk::fem::Element.
Definition at line 64 of file itkFEMElementStd.h.
typedef Superclass::MatrixType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::MatrixType [inherited] |
Reimplemented from itk::fem::Element.
Reimplemented in itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 62 of file itkFEMElementStd.h.
typedef Superclass::Node itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::Node [inherited] |
Definition at line 68 of file itkFEMElementStd.h.
typedef Superclass::NodeIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::NodeIDType [inherited] |
Reimplemented from itk::fem::Element.
Definition at line 66 of file itkFEMElementStd.h.
Pointer or SmartPointer to an object.
Reimplemented from itk::fem::ElementStd< 2, 2 >.
Reimplemented in itk::fem::Element2DC0LinearLineStress, and itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 33 of file itkFEMElement2DC0LinearLine.h.
Standard Self typedef.
Reimplemented from itk::fem::ElementStd< 2, 2 >.
Reimplemented in itk::fem::Element2DC0LinearLineStress, and itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 33 of file itkFEMElement2DC0LinearLine.h.
Standard Superclass typedef.
Reimplemented from itk::fem::ElementStd< 2, 2 >.
Reimplemented in itk::fem::Element2DC0LinearLineStress, and itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 33 of file itkFEMElement2DC0LinearLine.h.
typedef Superclass::VectorType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::VectorType [inherited] |
Reimplemented from itk::fem::Element.
Reimplemented in itk::fem::Element1DStress< Element2DC0LinearLine >.
Definition at line 63 of file itkFEMElementStd.h.
anonymous enum |
Methods related to numeric integration
Definition at line 42 of file itkFEMElement2DC0LinearLine.h.
anonymous enum [inherited] |
Constant that represents an invalid DegreeOfFreedomID object. If a degree of freedom is assigned this value, this means that that no specific value was (yet) assigned to this DOF.
Definition at line 125 of file itkFEMElementBase.h.
anonymous enum [inherited] |
Maximum supported order of 1D Gauss-Legendre integration. Integration points are defined for orders from 1 to gaussMaxOrder. Number of integration points is equal to the order of integration rule.
Definition at line 473 of file itkFEMElementBase.h.
anonymous enum [inherited] |
Definition at line 69 of file itkFEMElementStd.h.
anonymous enum [inherited] |
Number of nodes that define the element.
Definition at line 74 of file itkFEMElementStd.h.
anonymous enum [inherited] |
Number of dimensions of space in which element can exist.
Definition at line 79 of file itkFEMElementStd.h.
virtual int itk::fem::FEMLightObject::ClassID | ( | ) | const [pure virtual, inherited] |
Returns the class ID of the object. This function is used to determine the class of the object without having to use the dynamic_cast operator.
Implemented in itk::fem::FiniteDifferenceFunctionLoad< TMoving, TFixed >, itk::fem::Element2DC0LinearLineStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element::Node, itk::fem::ImageMetricLoad< TMoving, TFixed >, itk::fem::LoadBC, itk::fem::LoadBCMFC, itk::fem::LoadEdge, itk::fem::LoadElement, itk::fem::LoadGravConst, itk::fem::LoadLandmark, itk::fem::LoadNode, itk::fem::LoadPoint, itk::fem::LoadTest< TClass >, and itk::fem::MaterialLinearElasticity.
virtual Baseclass::Pointer itk::fem::FEMLightObject::Clone | ( | ) | const [pure virtual, inherited] |
Duplicates the currect object. This function must be implemented by every derived class to create an exact copy of an object. The function returns a pointer to a base class.
Implemented in itk::fem::FiniteDifferenceFunctionLoad< TMoving, TFixed >, itk::fem::Element2DC0LinearLineStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element::Node, itk::fem::ImageMetricLoad< TMoving, TFixed >, itk::fem::LoadBC, itk::fem::LoadBCMFC, itk::fem::LoadEdge, itk::fem::LoadElement, itk::fem::LoadGravConst, itk::fem::LoadLandmark, itk::fem::LoadNode, itk::fem::LoadPoint, itk::fem::LoadTest< TClass >, and itk::fem::MaterialLinearElasticity.
static FEMLightObject::Pointer itk::fem::FEMLightObject::CreateFromStream | ( | std::istream & | f, | |
void * | info | |||
) | [static, inherited] |
Read object of any derived type from stream.
This static function creates an object of a class, which is derived from FEMLightObject. The class of object is first determined from the stream, then the object of that class is constructed using the FEMObjectFactory. Finally the data for this object is read from the stream, by calling the Read() member function.
DegreeOfFreedomIDType itk::fem::Element::GetDegreeOfFreedom | ( | unsigned int | local_dof | ) | const [inline, inherited] |
Convenient way to access IDs of degrees of freedom that are stored in node objects.
local_dof | Local number of degree of freedom within an element. |
Definition at line 389 of file itkFEMElementBase.h.
References itk::fem::Element::Node::GetDegreeOfFreedom(), itk::fem::Element::GetNode(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode(), and itk::fem::Element::InvalidDegreeOfFreedomID.
virtual Float itk::fem::Element::GetElementDeformationEnergy | ( | MatrixType & | LocalSolution | ) | const [virtual, inherited] |
Compute the physical energy, U, of the deformation (e.g. stress / strain ).
T U = u Ke u
The matrix LocalSolution contains the solution to use in the energy computation. Usually, this is the solution at the nodes.
virtual VectorType itk::fem::Element::GetGlobalFromLocalCoordinates | ( | const VectorType & | pt | ) | const [virtual, inherited] |
Transforms the given local element coordinates into global.
pt | Point in local element coordinates. |
virtual void itk::fem::Element2DC0LinearLine::GetIntegrationPointAndWeight | ( | unsigned int | i, | |
VectorType & | pt, | |||
Float & | w, | |||
unsigned int | order | |||
) | const [virtual] |
Methods related to numeric integration Computes the vector representing the i-th integration point in local element coordinates for a Gauss-Legendre numerical integration over the element domain. It also computes the weight at this integration point.
Optionally you can also specify the order of integration. If order is not specified, it defaults to 0, which means that the derived element should use the optimal integration order specific for that element.
i | Integration point number 0<=i<GetNumberOfIntegrationPoints() | |
pt | Reference to object of class VectorType that will hold the integration point. | |
w | Reference to Float variable that will hold the weight. | |
order | Order of integration. |
Implements itk::fem::Element.
virtual void itk::fem::Element::GetLandmarkContributionMatrix | ( | float | eta, | |
MatrixType & | Le | |||
) | const [virtual, inherited] |
Compute and return landmark contribution to element stiffness matrix (Le) in global coordinate system.
b T int (1/eta)^2 N(x) N(x) dx a
where (eta ) is the landmark weight. Implementation is similar to GetMassMatrix.
virtual void itk::fem::Element::GetLoadVector | ( | LoadPointer | l, | |
VectorType & | Fe | |||
) | const [pure virtual, inherited] |
Compute and return the element load vector for a given external load. The class of load object determines the type of load acting on the elemnent. Basically this is the contribution of this element on the right side of the master matrix equation, due to the specified load. Returned vector includes only nodal forces that correspond to the given Load object.
Visitor design pattern is used in the loads implementation. This function only selects and calls the proper function based on the given class of load object. The code that performs the actual conversion to the corresponding nodal loads is defined elswhere.
For example on how to define specific element load, see funtion LoadImplementationPoint_Bar2D.
l | Pointer to a load object. | |
Fe | Reference to vector object that will store nodal forces. |
virtual bool itk::fem::Element2DC0LinearLine::GetLocalFromGlobalCoordinates | ( | const VectorType & | globalPt, | |
VectorType & | localPt | |||
) | const [virtual] |
Transforms the given global element coordinates into local. Returns false if the point is outside.
globalPt | Reference to vector containing a point in global (world) coordinates. | |
localPt | Reference to the vector that will store the local coordinate. |
Implements itk::fem::Element.
virtual void itk::fem::Element::GetMassMatrix | ( | MatrixType & | Me | ) | const [virtual, inherited] |
Compute and return element mass matrix (Me) in global coordinate system.
b T int N(x) (rho c) N(x) dx a
where (rho c) is constant (element density), which is here assumed to be equal to one. If this is not the case, this function must be overriden in a derived class. Implementation is similar to GetStiffnessMatrix.
Reimplemented in itk::fem::Element2DC0LinearLineStress, itk::fem::Element2DC1Beam, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, and itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >.
virtual Material::ConstPointer itk::fem::Element::GetMaterial | ( | void | ) | const [inline, virtual, inherited] |
Return the pointer to the Material object used by the element. All derived classes, which use objects of Material class should override this method to provide access to the material from the base class.
Reimplemented in itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
Definition at line 412 of file itkFEMElementBase.h.
virtual void itk::fem::Element::GetMaterialMatrix | ( | MatrixType & | D | ) | const [pure virtual, inherited] |
Compute the element material matrix.
D | Reference to a matrix object |
Implemented in itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
virtual NodeIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNode | ( | unsigned int | n | ) | const [inline, virtual, inherited] |
Implements itk::fem::Element.
Definition at line 93 of file itkFEMElementStd.h.
virtual const VectorType& itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNodeCoordinates | ( | unsigned int | n | ) | const [inline, virtual, inherited] |
Implements itk::fem::Element.
Definition at line 111 of file itkFEMElementStd.h.
virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedom | ( | void | ) | const [inline, virtual, inherited] |
Return the total number of degrees of freedom defined in a derived element class. By default this is equal to number of points in a cell multiplied by number of degrees of freedom at each point.
Definition at line 650 of file itkFEMElementBase.h.
References itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode(), and itk::fem::Element::GetNumberOfNodes().
Referenced by itk::fem::Element::GetDegreeOfFreedom().
virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode | ( | void | ) | const [pure virtual, inherited] |
Return the number of degrees of freedom at each node. This is also equal to number of unknowns that we want to solve for at each point within an element.
Implemented in itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
Referenced by itk::fem::Element::GetDegreeOfFreedom(), and itk::fem::Element::GetNumberOfDegreesOfFreedom().
virtual unsigned int itk::fem::Element2DC0LinearLine::GetNumberOfIntegrationPoints | ( | unsigned int | order | ) | const [virtual] |
Returns total number of integration points, for given order of Gauss-Legendre numerical integration rule.
Implements itk::fem::Element.
virtual unsigned int itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNumberOfNodes | ( | void | ) | const [inline, virtual, inherited] |
Methods that define the geometry of an element
Implements itk::fem::Element.
Definition at line 90 of file itkFEMElementStd.h.
virtual unsigned int itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNumberOfSpatialDimensions | ( | ) | const [inline, virtual, inherited] |
Implements itk::fem::Element.
Definition at line 116 of file itkFEMElementStd.h.
virtual void itk::fem::Element::GetStiffnessMatrix | ( | MatrixType & | Ke | ) | const [virtual, inherited] |
Compute and return element stiffnes matrix (Ke) in global coordinate system. The base class provides a general implementation which only computes
b T int B(x) D B(x) dx a
using the Gaussian numeric integration method. The function calls GetIntegrationPointAndWeight() / GetNumberOfIntegrationPoints() to obtain the integration points. It also calls the GetStrainDisplacementMatrix() and GetMaterialMatrix() member functions.
Ke | Reference to the resulting stiffnes matrix. |
Reimplemented in itk::fem::Element2DC1Beam, and itk::fem::Element1DStress< Element2DC0LinearLine >.
virtual void itk::fem::Element::GetStrainDisplacementMatrix | ( | MatrixType & | B, | |
const MatrixType & | shapeDgl | |||
) | const [pure virtual, inherited] |
Compute the strain displacement matrix at local point.
B | Reference to a matrix object that will contain the result | |
shapeDgl | Matrix that contains derivatives of shape functions w.r.t. global coordinates. |
Implemented in itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
virtual VectorType itk::fem::Element::GetStrainsAtPoint | ( | const VectorType & | pt, | |
const Solution & | sol, | |||
unsigned int | index | |||
) | const [virtual, inherited] |
virtual VectorType itk::fem::Element::GetStressesAtPoint | ( | const VectorType & | pt, | |
const VectorType & | e, | |||
const Solution & | sol, | |||
unsigned int | index | |||
) | const [virtual, inherited] |
virtual VectorType itk::fem::Element::InterpolateSolution | ( | const VectorType & | pt, | |
const Solution & | sol, | |||
unsigned int | solutionIndex = 0 | |||
) | const [virtual, inherited] |
Return interpolated value of all unknown functions at given local point.
pt | Point in local element coordinates. | |
sol | Reference to the master solution object. This object is created by the Solver object when the whole FEM problem is solved and contains the values of unknown functions at nodes (degrees of freedom). | |
solutionIndex | We allow more than one solution vector to be stored - this selects which to use in interpolation. |
virtual Float itk::fem::Element::InterpolateSolutionN | ( | const VectorType & | pt, | |
const Solution & | sol, | |||
unsigned int | f, | |||
unsigned int | solutionIndex = 0 | |||
) | const [virtual, inherited] |
Return interpolated value of f-th unknown function at given local point.
pt | Point in local element coordinates. | |
sol | Reference to the master solution object. This object is created by the Solver object when the whole FEM problem is solved and contains the values of unknown functions at nodes (degrees of freedom). | |
f | Number of unknown function to interpolate. Must be 0 <= f < GetNumberOfDegreesOfFreedomPerNode(). | |
solutionIndex | We allow more than one solution vector to be stored - this selects which to use in interpolation. |
virtual void itk::fem::Element2DC0LinearLine::Jacobian | ( | const VectorType & | pt, | |
MatrixType & | J, | |||
const MatrixType * | pshapeD = 0 | |||
) | const [virtual] |
We need to provide our own implementation of calculating Jacobian, because the element lives in 2D space and has only one dimension. The default implementation of Jacobian in the Element base class is not correct since it assumes that the number of element dimensions is equal to the number of spatial dimensions.
Jacobian is a scalar for this element.
Reimplemented from itk::fem::Element.
virtual Float itk::fem::Element::JacobianDeterminant | ( | const VectorType & | pt, | |
const MatrixType * | pJ = 0 | |||
) | const [virtual, inherited] |
Compute the determinant of the Jacobian matrix at a given point with respect to the local coordinate system.
pt | Point in local element coordinates. | |
pJ | Optional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary. |
Reimplemented in itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element2DC1Beam.
virtual void itk::fem::Element::JacobianInverse | ( | const VectorType & | pt, | |
MatrixType & | invJ, | |||
const MatrixType * | pJ = 0 | |||
) | const [virtual, inherited] |
Compute the inverse of the Jacobian matrix at a given point with respect to the local coordinate system.
pt | Point in local element coordinates. | |
invJ | Reference to the object of MatrixType that will store the computed inverse if Jacobian. | |
pJ | Optional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary. |
Reimplemented in itk::fem::Element2DC0LinearTriangular, and itk::fem::Element2DC0QuadraticTriangular.
virtual void itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::Read | ( | std::istream & | , | |
void * | info | |||
) | [virtual, inherited] |
Methods related to I/O Read data for this class from input stream
Reimplemented from itk::fem::FEMLightObject.
Reimplemented in itk::fem::Element2DC1Beam, and itk::fem::Element1DStress< Element2DC0LinearLine >.
virtual void itk::fem::Element::SetMaterial | ( | Material::ConstPointer | ) | [inline, virtual, inherited] |
Set the pointer to the Material object used by the element. All derived classes, which use objects of Material class should override this method to provide access to the material from the base class.
Reimplemented in itk::fem::Element2DC1Beam, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
Definition at line 422 of file itkFEMElementBase.h.
virtual void itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::SetNode | ( | unsigned int | n, | |
NodeIDType | node | |||
) | [inline, virtual, inherited] |
Implements itk::fem::Element.
Definition at line 102 of file itkFEMElementStd.h.
virtual void itk::fem::Element2DC0LinearLine::ShapeFunctionDerivatives | ( | const VectorType & | pt, | |
MatrixType & | shapeD | |||
) | const [virtual] |
Compute the matrix of values of the shape functions derivatives with respect to local coordinates of this element at a given point.
A column in this matrix corresponds to a specific shape function, while a row corresponds to different local coordinates. E.g. element at row 2, col 3 contains derivative of shape function number 3 with respect to local coordinate number 2.
pt | Point in local element coordinates. | |
shapeD | Reference to a matrix object, which will be filled with values of shape function derivatives. |
Implements itk::fem::Element.
virtual void itk::fem::Element::ShapeFunctionGlobalDerivatives | ( | const VectorType & | pt, | |
MatrixType & | shapeDgl, | |||
const MatrixType * | pJ = 0 , |
|||
const MatrixType * | pshapeD = 0 | |||
) | const [virtual, inherited] |
Compute matrix of shape function derivatives with respect to global coordinates.
A column in this matrix corresponds to a specific shape function, while a row corresponds to different global coordinates.
pt | Point in local element coordinates. | |
shapeDgl | Reference to a matrix object, which will be filled with values of shape function derivatives w.r.t. global (world) element coordinates. | |
pJ | Optional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary. | |
pshapeD | A pointer to derivatives of shape functions at point pt. If this pointer is 0, derivatives will be computed as necessary. |
virtual VectorType itk::fem::Element2DC0LinearLine::ShapeFunctions | ( | const VectorType & | pt | ) | const [virtual] |
Methods related to the geometry of an element
Implements itk::fem::Element.
static void itk::fem::FEMLightObject::SkipWhiteSpace | ( | std::istream & | f | ) | [static, inherited] |
Helper function that skips all the whitespace and comments in an input stream.
virtual void itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::Write | ( | std::ostream & | f | ) | const [virtual, inherited] |
Write data for this class to output stream
Reimplemented from itk::fem::FEMLightObject.
Reimplemented in itk::fem::Element2DC1Beam, and itk::fem::Element1DStress< Element2DC0LinearLine >.
const Float itk::fem::Element::gaussPoint[gaussMaxOrder+1][gaussMaxOrder] [static, inherited] |
Points for 1D Gauss-Legendre integration from -1 to 1. First index is order of integration, second index is the number of integration point.
Example: gaussPoint[4][2] returns third point of the 4th order integration rule. Subarray gaussPoint[0][...] does not provide useful information. It is there only to keep order index correct.
Definition at line 486 of file itkFEMElementBase.h.
const Float itk::fem::Element::gaussWeight[gaussMaxOrder+1][gaussMaxOrder] [static, inherited] |
Weights for Gauss-Legendre integration.
Definition at line 493 of file itkFEMElementBase.h.
int itk::fem::FEMLightObject::GN [inherited] |
Global number of an object (ID of an object) In general the ID's are required to be unique only within a specific type of derived classes (Elements, Nodes, ...) If the GN is not required, it can be ignored. (normally you need the GN when writing or reading objects to/from stream.
Definition at line 165 of file itkFEMLightObject.h.
Referenced by itk::fem::FEMLightObject::FEMLightObject().
NodeIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::m_node[NumberOfNodes] [protected, inherited] |
Array of pointers to point objects that define the element
Definition at line 141 of file itkFEMElementStd.h.
const std::string itk::fem::FEMLightObject::whitespaces [static, inherited] |
Const string of all whitespace characters. This string is used by SkipWhiteSpace function.
Definition at line 135 of file itkFEMLightObject.h.