ITK  4.1.0
Insight Segmentation and Registration Toolkit
Classes | Public Types | Public Member Functions | Static Public Attributes | Protected Member Functions | Protected Attributes
itk::fem::Element Class Reference

#include <itkFEMElementBase.h>

+ Inheritance diagram for itk::fem::Element:
+ Collaboration diagram for itk::fem::Element:

List of all members.

Classes

class  Node
 Class that stores information required to define a node. More...

Public Types

enum  { InvalidDegreeOfFreedomID = 0xffffffff }
enum  { gaussMaxOrder = 10 }
typedef FEMPArray< ElementArrayType
typedef VectorContainer
< ElementIdentifier,
Element::Pointer
ArrayType1
typedef SmartPointer< const SelfConstPointer
typedef unsigned int DegreeOfFreedomIDType
typedef unsigned long ElementIdentifier
typedef double Float
typedef vnl_matrix< FloatMatrixType
typedef Node::ConstPointer NodeIDType
typedef SmartPointer< SelfPointer
typedef Element Self
typedef FEMLightObject Superclass
typedef vnl_vector< FloatVectorType
typedef FEMLightObject LoadType
typedef LoadType::Pointer LoadPointer

Public Member Functions

virtual std::vector
< std::vector< int > > 
GetEdgeIds (void) const
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=0) const =0
virtual void GetLandmarkContributionMatrix (float eta, MatrixType &Le) const
virtual bool GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const =0
virtual void GetMassMatrix (MatrixType &Me) const
virtual Material::ConstPointer GetMaterial (void) const
virtual void GetMaterialMatrix (MatrixType &D) const =0
virtual const char * GetNameOfClass () const
virtual NodeIDType GetNode (unsigned int n) const =0
virtual const VectorTypeGetNodeCoordinates (unsigned int n) const =0
virtual unsigned int GetNumberOfDegreesOfFreedom (void) const
virtual unsigned int GetNumberOfDegreesOfFreedomPerNode (void) const =0
virtual unsigned int GetNumberOfIntegrationPoints (unsigned int order=0) const =0
virtual unsigned int GetNumberOfNodes (void) const =0
virtual unsigned int GetNumberOfSpatialDimensions () const =0
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 PopulateEdgeIds (void)=0
virtual void SetMaterial (Material::ConstPointer)
virtual void SetNode (unsigned int n, NodeIDType node)=0
virtual void SetNode (unsigned int n, Node::Pointer node)
virtual void ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const =0
virtual void ShapeFunctionGlobalDerivatives (const VectorType &pt, MatrixType &shapeDgl, const MatrixType *pJ=0, const MatrixType *pshapeD=0) const
virtual VectorType ShapeFunctions (const VectorType &pt) const =0
DegreeOfFreedomIDType GetDegreeOfFreedom (unsigned int local_dof) const

Static Public Attributes

static const Float gaussPoint [gaussMaxOrder+1][gaussMaxOrder]
static const Float gaussWeight [gaussMaxOrder+1][gaussMaxOrder]

Protected Member Functions

virtual void PrintSelf (std::ostream &os, Indent indent) const

Protected Attributes

std::vector< std::vector< int > > m_EdgeIds

Detailed Description

Abstract base element class.

Derive this class to create new finite element classes. The storage of element parameters (geometry...) can't be implemented here, since we don't know yet, how much memory each element needs. Instead each derived class should take care of the memory management (declare appropriate data members) for the element parameters and provide access to these parameters (like nodes, materials...).

Derived classes must define the following class methods: GetIntegrationPointAndWeight GetNumberOfIntegrationPoints ShapeFunctions ShapeFunctionDerivatives GetLocalFromGlobalCoordinates JacobianDeterminant JacobianInverse PopulateEdgeIds

These are required for the loads to be properly applied properly to the element.

See also:
Element2DC0LinearLine
Element2DC0LinearQuadrilateral
Element2DC0LinearTriangular
Element2DC1Beam
Element2DC0QuadraticTriangular
Element3DC0LinearHexahedron
Element3DC0LinearTetrahedron
Element3DC0LinearTriangular
Element3DC0LinearTriangularLaplaceBeltrami

Definition at line 72 of file itkFEMElementBase.h.


Member Typedef Documentation

Array class that holds special pointers to the Element objects

Definition at line 94 of file itkFEMElementBase.h.

Definition at line 95 of file itkFEMElementBase.h.

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLine, and itk::fem::Element2DC0LinearLineStress.

Definition at line 79 of file itkFEMElementBase.h.

typedef unsigned long itk::fem::Element::ElementIdentifier

Definition at line 88 of file itkFEMElementBase.h.

typedef double itk::fem::Element::Float

Easy and consistent access to LoadElement and LoadElement::Pointer type. This is a pointer to FEMLightObject to avoid cyclic references between LoadElement and Element classes. As a consequence whenever you need to use a pointer to LoadElement class within the element's declaration or definition, ALWAYS use this typedef instead. When calling the GetLoadVector(...) function from outside, you should ALWAYS first convert the argument to Element::LoadPointer. See code of function Solver::AssembleF(...) for more info.

Reimplemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

Definition at line 119 of file itkFEMElementBase.h.

Easy and consistent access to LoadElement and LoadElement::Pointer type. This is a pointer to FEMLightObject to avoid cyclic references between LoadElement and Element classes. As a consequence whenever you need to use a pointer to LoadElement class within the element's declaration or definition, ALWAYS use this typedef instead. When calling the GetLoadVector(...) function from outside, you should ALWAYS first convert the argument to Element::LoadPointer. See code of function Solver::AssembleF(...) for more info.

Reimplemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

Definition at line 118 of file itkFEMElementBase.h.

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLine, and itk::fem::Element2DC0LinearLineStress.

Definition at line 78 of file itkFEMElementBase.h.

Standard class typedefs.

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLine, and itk::fem::Element2DC0LinearLineStress.

Definition at line 76 of file itkFEMElementBase.h.

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLine, and itk::fem::Element2DC0LinearLineStress.

Definition at line 77 of file itkFEMElementBase.h.


Member Enumeration Documentation

anonymous enum

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.

Enumerator:
InvalidDegreeOfFreedomID 

Definition at line 133 of file itkFEMElementBase.h.

anonymous enum

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.

See also:
gaussPoint
Enumerator:
gaussMaxOrder 

Definition at line 517 of file itkFEMElementBase.h.


Member Function Documentation

DegreeOfFreedomIDType itk::fem::Element::GetDegreeOfFreedom ( unsigned int  local_dof) const [inline]

Convenient way to access IDs of degrees of freedom that are stored in node objects.

Parameters:
local_dofLocal number of degree of freedom within an element.

Definition at line 420 of file itkFEMElementBase.h.

References GetNode(), GetNumberOfDegreesOfFreedom(), GetNumberOfDegreesOfFreedomPerNode(), and InvalidDegreeOfFreedomID.

virtual std::vector<std::vector<int> > itk::fem::Element::GetEdgeIds ( void  ) const [inline, virtual]

Access the edge ids vector. The vector in turn contains a list of edge ids.

Definition at line 706 of file itkFEMElementBase.h.

References m_EdgeIds.

virtual Float itk::fem::Element::GetElementDeformationEnergy ( MatrixType LocalSolution) const [virtual]

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.

Transforms the given local element coordinates into global.

Parameters:
ptPoint in local element coordinates.
virtual void itk::fem::Element::GetIntegrationPointAndWeight ( unsigned int  i,
VectorType pt,
Float w,
unsigned int  order = 0 
) const [pure 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.

Note:
This function must be implemented in derived element classes, and is expected to provide valid integration points for up to gaussMaxOrder-th order of integration.
Parameters:
iIntegration point number 0<=i<GetNumberOfIntegrationPoints()
ptReference to object of class VectorType that will hold the integration point.
wReference to Float variable that will hold the weight.
orderOrder of integration.
See also:
GetNumberOfIntegrationPoints()

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element3DC0LinearTriangular, and itk::fem::Element2DC0LinearLine.

virtual void itk::fem::Element::GetLandmarkContributionMatrix ( float  eta,
MatrixType Le 
) const [virtual]

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 bool itk::fem::Element::GetLocalFromGlobalCoordinates ( const VectorType globalPt,
VectorType localPt 
) const [pure virtual]

Transforms the given global element coordinates into local. Returns false if the point is outside.

Parameters:
globalPtReference to vector containing a point in global (world) coordinates.
localPtReference to the vector that will store the local coordinate.

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element3DC0LinearTriangular, and itk::fem::Element2DC0LinearLine.

virtual void itk::fem::Element::GetMassMatrix ( MatrixType Me) const [virtual]
virtual Material::ConstPointer itk::fem::Element::GetMaterial ( void  ) const [inline, virtual]

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.

Note:
Derived Element classes don't have to use a material class, but since the majority of the final Element classes uses Material classes to specify phhysical constants that the element depends on, we provide this virtual function that enables easy access to this pointer from the base class. If the derived class does not override this function, the returned pointer is 0 by default, signaling that there is no Material object.
See also:
SetMaterial

Reimplemented in itk::fem::Element2DC1Beam, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.

Definition at line 448 of file itkFEMElementBase.h.

virtual void itk::fem::Element::GetMaterialMatrix ( MatrixType D) const [pure virtual]
virtual const char* itk::fem::Element::GetNameOfClass ( ) const [virtual]

Run-time type information (and related methods).

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLineStress, and itk::fem::Element2DC0LinearLine.

virtual NodeIDType itk::fem::Element::GetNode ( unsigned int  n) const [pure virtual]
virtual const VectorType& itk::fem::Element::GetNodeCoordinates ( unsigned int  n) const [pure virtual]

Return a vector of global coordinates of n-th node in an element.

Parameters:
nLocal number of node. Must be 0 <= n < this->GetNumberOfNodes().

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedom ( void  ) const [inline, virtual]

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 698 of file itkFEMElementBase.h.

References GetNumberOfDegreesOfFreedomPerNode(), and GetNumberOfNodes().

Referenced by GetDegreeOfFreedom().

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode ( void  ) const [pure virtual]
virtual unsigned int itk::fem::Element::GetNumberOfIntegrationPoints ( unsigned int  order = 0) const [pure virtual]

Returns total number of integration points, for given order of Gauss-Legendre numerical integration rule.

Note:
This function must be implemented in derived element classes, and is expected to provide valid number of integration points for up to gaussMaxOrder-th order of integration.
See also:
GetIntegrationPointAndWeight()

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element3DC0LinearTriangular, and itk::fem::Element2DC0LinearLine.

virtual unsigned int itk::fem::Element::GetNumberOfNodes ( void  ) const [pure virtual]
virtual unsigned int itk::fem::Element::GetNumberOfSpatialDimensions ( ) const [pure virtual]

Returns the number of dimensions of space in which the element is defined. e.g. 2 for 2D elements, 3 for 3D... This is also equal to the size vector containing nodal coordinates.

Implemented in itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

virtual void itk::fem::Element::GetStiffnessMatrix ( MatrixType Ke) const [virtual]

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.

Parameters:
KeReference to the resulting stiffnes matrix.
Note:
This is a very generic implementation of the stiffness matrix that is suitable for any problem/element definition. A specifc element may override this implementation with its own simple one.

Reimplemented in itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, and itk::fem::Element2DC1Beam.

virtual void itk::fem::Element::GetStrainDisplacementMatrix ( MatrixType B,
const MatrixType shapeDgl 
) const [pure virtual]
virtual VectorType itk::fem::Element::GetStrainsAtPoint ( const VectorType pt,
const Solution sol,
unsigned int  index 
) const [virtual]
virtual VectorType itk::fem::Element::GetStressesAtPoint ( const VectorType pt,
const VectorType e,
const Solution sol,
unsigned int  index 
) const [virtual]
virtual VectorType itk::fem::Element::InterpolateSolution ( const VectorType pt,
const Solution sol,
unsigned int  solutionIndex = 0 
) const [virtual]

Return interpolated value of all unknown functions at given local point.

Parameters:
ptPoint in local element coordinates.
solReference 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).
solutionIndexWe 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]

Return interpolated value of f-th unknown function at given local point.

Parameters:
ptPoint in local element coordinates.
solReference 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).
fNumber of unknown function to interpolate. Must be 0 <= f < GetNumberOfDegreesOfFreedomPerNode().
solutionIndexWe allow more than one solution vector to be stored - this selects which to use in interpolation.
virtual void itk::fem::Element::Jacobian ( const VectorType pt,
MatrixType J,
const MatrixType pshapeD = 0 
) const [virtual]

Compute the Jacobian matrix of the transformation from local to global coordinates at a given local point.

A column in this matrix corresponds to a global coordinate, while a row corresponds to different local coordinates. E.g. element at row 2, col 3 contains derivative of the third global coordinate with respect to local coordinate number 2.

In order to compute the Jacobian, we normally need the shape function derivatives. If they are known, you should pass a pointer to an object of MatrixType that contains the shape function derivatives. If they are not known, pass null pointer and they will be computed automatically.

Parameters:
ptPoint in local coordinates
Jreferece to matrix object, which will contain the jacobian
pshapeDA pointer to derivatives of shape functions at point pt. If this pointer is 0, derivatives will be computed as necessary.

Reimplemented in itk::fem::Element2DC0LinearLine.

virtual Float itk::fem::Element::JacobianDeterminant ( const VectorType pt,
const MatrixType pJ = 0 
) const [virtual]

Compute the determinant of the Jacobian matrix at a given point with respect to the local coordinate system.

Parameters:
ptPoint in local element coordinates.
pJOptional 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::Element2DC1Beam, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearTriangular.

virtual void itk::fem::Element::JacobianInverse ( const VectorType pt,
MatrixType invJ,
const MatrixType pJ = 0 
) const [virtual]

Compute the inverse of the Jacobian matrix at a given point with respect to the local coordinate system.

Parameters:
ptPoint in local element coordinates.
invJReference to the object of MatrixType that will store the computed inverse if Jacobian.
pJOptional 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::Element3DC0LinearTriangular.

virtual void itk::fem::Element::PopulateEdgeIds ( void  ) [pure virtual]
virtual void itk::fem::Element::PrintSelf ( std::ostream &  os,
Indent  indent 
) const [protected, virtual]

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element2DC1Beam, itk::fem::ElementStd< 3, 2 >, itk::fem::ElementStd< 2, 2 >, itk::fem::ElementStd< 8, 3 >, itk::fem::ElementStd< 6, 2 >, itk::fem::ElementStd< 4, 3 >, itk::fem::ElementStd< 4, 2 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element2DC0LinearLineStress, and itk::fem::Element3DC0LinearTriangularMembrane.

virtual void itk::fem::Element::SetMaterial ( Material::ConstPointer  ) [inline, virtual]
virtual void itk::fem::Element::SetNode ( unsigned int  n,
NodeIDType  node 
) [pure virtual]
virtual void itk::fem::Element::SetNode ( unsigned int  n,
Node::Pointer  node 
) [inline, virtual]
virtual void itk::fem::Element::ShapeFunctionDerivatives ( const VectorType pt,
MatrixType shapeD 
) const [pure 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.

Parameters:
ptPoint in local element coordinates.
shapeDReference to a matrix object, which will be filled with values of shape function derivatives.
See also:
ShapeFunctionGlobalDerivatives

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element3DC0LinearTriangular, and itk::fem::Element2DC0LinearLine.

virtual void itk::fem::Element::ShapeFunctionGlobalDerivatives ( const VectorType pt,
MatrixType shapeDgl,
const MatrixType pJ = 0,
const MatrixType pshapeD = 0 
) const [virtual]

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.

Parameters:
ptPoint in local element coordinates.
shapeDglReference to a matrix object, which will be filled with values of shape function derivatives w.r.t. global (world) element coordinates.
pJOptional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary.
pshapeDA pointer to derivatives of shape functions at point pt. If this pointer is 0, derivatives will be computed as necessary.
See also:
ShapeFunctionDerivatives
virtual VectorType itk::fem::Element::ShapeFunctions ( const VectorType pt) const [pure virtual]

Returns a vector containing the values of all shape functions that define the geometry of a finite element at a given local point within an element.

Parameters:
ptPoint in local element coordinates.

Implemented in itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element3DC0LinearTriangular, and itk::fem::Element2DC0LinearLine.


Member Data Documentation

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.

See also:
gaussWeight

Definition at line 530 of file itkFEMElementBase.h.

Weights for Gauss-Legendre integration.

See also:
gaussPoint

Definition at line 537 of file itkFEMElementBase.h.

std::vector<std::vector<int> > itk::fem::Element::m_EdgeIds [protected]

Definition at line 726 of file itkFEMElementBase.h.

Referenced by GetEdgeIds().


The documentation for this class was generated from the following file: