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itk::fem::Element Class Reference

Abstract base element class. More...

#include <itkFEMElementBase.h>

Inheritance diagram for itk::fem::Element:

[legend]Collaboration diagram for itk::fem::Element:

[legend]List of all members.


Public Types
typedef Element	Self
typedef FEMLightObject	Superclass
typedef Self *	Pointer
typedef const Self *	ConstPointer
typedef double	Float
typedef FEMPArray< Element >	ArrayType
typedef vnl_matrix< Float >	MatrixType
typedef vnl_vector< Float >	VectorType
typedef unsigned int	DegreeOfFreedomIDType
typedef Node::ConstPointer	NodeIDType
enum	{ InvalidDegreeOfFreedomID = 0xffffffff }
enum	{ gaussMaxOrder = 10 }

typedef FEMLightObject	LoadType
typedef LoadType::Pointer	LoadPointer
Public Member Functions
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 void	GetStiffnessMatrix (MatrixType &Ke) const
virtual Float	GetElementDeformationEnergy (MatrixType &LocalSolution) const
virtual void	GetMassMatrix (MatrixType &Me) const
virtual void	GetLandmarkContributionMatrix (float eta, MatrixType &Le) const
virtual void	GetLoadVector (LoadPointer l, VectorType &Fe) const =0
virtual void	GetStrainDisplacementMatrix (MatrixType &B, const MatrixType &shapeDgl) const =0
virtual void	GetMaterialMatrix (MatrixType &D) const =0
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 Material::ConstPointer	GetMaterial (void) const
virtual void	SetMaterial (Material::ConstPointer)
virtual void	GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order=0) const =0
virtual unsigned int	GetNumberOfIntegrationPoints (unsigned int order=0) const =0
virtual unsigned int	GetNumberOfNodes (void) const =0
virtual NodeIDType	GetNode (unsigned int n) const =0
virtual void	SetNode (unsigned int n, NodeIDType node)=0
virtual const VectorType &	GetNodeCoordinates (unsigned int n) const =0
virtual VectorType	GetGlobalFromLocalCoordinates (const VectorType &pt) const
virtual bool	GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const =0
virtual unsigned int	GetNumberOfSpatialDimensions () const =0
virtual VectorType	ShapeFunctions (const VectorType &pt) const =0
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 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 unsigned int	GetNumberOfDegreesOfFreedom (void) const
virtual unsigned int	GetNumberOfDegreesOfFreedomPerNode (void) const =0

DegreeOfFreedomIDType	GetDegreeOfFreedom (unsigned int local_dof) const
Static Public Attributes
const Float	gaussPoint [gaussMaxOrder+1][gaussMaxOrder]
const Float	gaussWeight [gaussMaxOrder+1][gaussMaxOrder]

Detailed Description

Abstract base element class.

Derive this class to create new finite element classes. All derived classes must define:

Ke(): Function to calculate the element stiffness matrix in global coordinate system.
Fe(): Function to calculate the element force vector in global coordinate system.
uDOF(): Provide a pointer to storage of i-th DOF displacement in the element.
Clone(): Function that creates a duplicate of current element and returns a pointer to it.

and optionally (if required):

Read(): Reads element data from the stream f. assume that the stream position is already where the element data starts. Take care of the error checking.
Write(): Writes element data to the stream.
Draw(): Draws the element on the device context (Windows only).

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...).

Definition at line 77 of file itkFEMElementBase.h.

Member Typedef Documentation

typedef FEMPArray<Element> itk::fem::Element::ArrayType

Array class that holds special pointers to the Element objects Definition at line 90 of file itkFEMElementBase.h.
Referenced by itk::fem::ImageMetricLoad< TMoving, TFixed >::GetSolution(), and itk::fem::FiniteDifferenceFunctionLoad< MovingImageType, FixedImageType >::GetSolution().

typedef unsigned int itk::fem::Element::DegreeOfFreedomIDType

Type that stores global ID's of degrees of freedom.
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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 120 of file itkFEMElementBase.h.
Referenced by itk::fem::Element::Node::GetDegreeOfFreedom().

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

Floating point type used in all Element classes.
Reimplemented in 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 >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, 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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 85 of file itkFEMElementBase.h.
Referenced by SetMaterial().

typedef LoadType::Pointer itk::fem::Element::LoadPointer

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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 114 of file itkFEMElementBase.h.
Referenced by itk::fem::LoadImplementationGenericLandmarkLoad::HandleLoad(), itk::fem::LoadImplementationTest< TLoadClass >::impl(), and itk::fem::ImageMetricLoadImplementation< TLoadClass >::ImplementImageMetricLoad().

typedef FEMLightObject itk::fem::Element::LoadType

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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 113 of file itkFEMElementBase.h.

typedef vnl_matrix<Float> itk::fem::Element::MatrixType

Class used to store the element stiffness matrix
Reimplemented in 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 >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, 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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 95 of file itkFEMElementBase.h.

typedef Node::ConstPointer itk::fem::Element::NodeIDType

Type that is used to store IDs of a node. It is a pointer to Node objects.
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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 513 of file itkFEMElementBase.h.

typedef Element itk::fem::Element::Self

Standard Self typedef.
Reimplemented from itk::fem::FEMLightObject.

Reimplemented in itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0LinearLineStress, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC1Beam, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, 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 >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, 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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 79 of file itkFEMElementBase.h.

typedef vnl_vector<Float> itk::fem::Element::VectorType

Class to store the element load vector
Reimplemented in 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 >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, 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 >, and itk::fem::ElementStd< 4, 2 >.
Definition at line 100 of file itkFEMElementBase.h.
Referenced by itk::fem::LoadImplementationGenericLandmarkLoad::HandleLoad(), itk::fem::LoadImplementationTest< TLoadClass >::impl(), itk::fem::ImageMetricLoadImplementation< TLoadClass >::ImplementImageMetricLoad(), SetMaterial(), and itk::fem::LoadLandmark::SetPoint().

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.
Enumeration values:

InvalidDegreeOfFreedomID

Definition at line 127 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

Enumeration values:

gaussMaxOrder

Definition at line 481 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_dof Local number of degree of freedom within an element.

Definition at line 394 of file itkFEMElementBase.h.

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.

virtual VectorType itk::fem::Element::GetGlobalFromLocalCoordinates ( const VectorType & pt ) const [virtual]

Transforms the given local element coordinates into global.

Parameters:

pt Point in local element coordinates.

virtual void itk::fem::Element::GetIntegrationPointAndWeight ( unsigned int i,

VectorType & pt,

Float & w,

unsigned int order = 0

) const [pure virtual]

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:

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.

See also:
GetNumberOfIntegrationPoints()

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

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 void itk::fem::Element::GetLoadVector ( LoadPointer l,

VectorType & Fe

) const [pure virtual]

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.

Note:
Each derived class must implement its own version of this function. This is automated by calling the LOAD_FUNCTION() macro within the class declaration (in the public: block).
For example on how to define specific element load, see funtion LoadImplementationPoint_Bar2D.

Note:
: Before a load can be applied to an element, the function that implements a load must be registered with the VisitorDispactcher class.

Parameters:

l Pointer to a load object.

Fe Reference to vector object that will store nodal forces.

See also:
VisitorDispatcher

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:

globalPt Reference to vector containing a point in global (world) coordinates.

localPt Reference to the vector that will store the local coordinate.

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

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

Returns the ID (pointer) of n-th node in an element.
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 >, and itk::fem::ElementStd< 4, 2 >.

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:

n Local 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 >, and itk::fem::ElementStd< 4, 2 >.

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 658 of file itkFEMElementBase.h.

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

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

Return the total number of nodes in an elememnt.
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 >, and itk::fem::ElementStd< 4, 2 >.

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 >, and itk::fem::ElementStd< 4, 2 >.

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:

Ke Reference 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::Element2DC1Beam, and itk::fem::Element1DStress< Element2DC0LinearLine >.

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:

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]

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

Parameters:

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::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:

pt Point in local coordinates

J referece to matrix object, which will contain the jacobian

pshapeD A 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:

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]

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

Parameters:

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::Element::SetNode ( unsigned int n,

NodeIDType node

) [pure virtual]

Sets the pointe of n-th node in an element to node.
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 >, and itk::fem::ElementStd< 4, 2 >.

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:

pt Point in local element coordinates.

shapeD Reference to a matrix object, which will be filled with values of shape function derivatives.

See also:
ShapeFunctionGlobalDerivatives

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

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:

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.

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:

pt Point in local element coordinates.

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

Member Data Documentation

const Float itk::fem::Element::gaussPoint[gaussMaxOrder+1][gaussMaxOrder] [static]

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 494 of file itkFEMElementBase.h.

const Float itk::fem::Element::gaussWeight[gaussMaxOrder+1][gaussMaxOrder] [static]

Weights for Gauss-Legendre integration.

See also:
gaussPoint
Definition at line 501 of file itkFEMElementBase.h.

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

itkFEMElementBase.h

Generated at Sun Apr 1 03:20:48 2007 for ITK by

itk::fem::Element Class Reference

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