#include <itkFEMElementBase.h>

Inheritance diagram for itk::fem::Element:

Collaboration diagram for itk::fem::Element:

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 73 of file itkFEMElementBase.h.

Classes
class	Node

Public Types
enum	{ InvalidDegreeOfFreedomID = 0xffffffff }

typedef FEMPArray< Element >	ArrayType

typedef VectorContainer < ElementIdentifier, Element::Pointer >	ArrayType1

typedef SmartPointer< const Self >	ConstPointer

typedef unsigned int	DegreeOfFreedomIDType

typedef unsigned long	ElementIdentifier

typedef double	Float

typedef vnl_matrix< Float >	MatrixType

typedef Node::ConstPointer	NodeIDType

typedef SmartPointer< Self >	Pointer

typedef Element	Self

typedef FEMLightObject	Superclass

typedef vnl_vector< Float >	VectorType


typedef FEMLightObject	LoadType

typedef LoadType::Pointer	LoadPointer

Public Types inherited from itk::fem::FEMLightObject
typedef Self	Baseclass

typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef FEMLightObject	Self

typedef itk::LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

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 VectorType &	GetNodeCoordinates (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=nullptr) const

virtual Float	JacobianDeterminant (const VectorType &pt, const MatrixType *pJ=nullptr) const

virtual void	JacobianInverse (const VectorType &pt, MatrixType &invJ, const MatrixType *pJ=nullptr) 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=nullptr, const MatrixType pshapeD=nullptr) const

virtual VectorType	ShapeFunctions (const VectorType &pt) const =0


DegreeOfFreedomIDType	GetDegreeOfFreedom (unsigned int local_dof) const

Public Member Functions inherited from itk::fem::FEMLightObject
int	GetGlobalNumber () const

void	SetGlobalNumber (int)

Public Member Functions inherited from itk::LightObject
virtual Pointer	CreateAnother () const

virtual void	Delete ()

virtual int	GetReferenceCount () const

	itkCloneMacro (Self)

void	Print (std::ostream &os, Indent indent=0) const

virtual void	Register () const

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const noexcept

Static Public Attributes
static const unsigned int	gaussMaxOrder = 10

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 override

Protected Member Functions inherited from itk::fem::FEMLightObject
	FEMLightObject ()

	FEMLightObject (const FEMLightObject &o)

virtual	~FEMLightObject () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

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

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

virtual	~LightObject ()

Protected Attributes
std::vector< std::vector< int > >	m_EdgeIds

Protected Attributes inherited from itk::fem::FEMLightObject
int	m_GlobalNumber

Protected Attributes inherited from itk::LightObject
AtomicInt< int >	m_ReferenceCount

Additional Inherited Members
Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Member Typedef Documentation

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

Array class that holds special pointers to the Element objects

Definition at line 95 of file itkFEMElementBase.h.

typedef VectorContainer<ElementIdentifier, Element::Pointer> itk::fem::Element::ArrayType1

Definition at line 96 of file itkFEMElementBase.h.

typedef SmartPointer<const Self> itk::fem::Element::ConstPointer

Definition at line 80 of file itkFEMElementBase.h.

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

Type that stores global ID's of degrees of freedom.

Definition at line 127 of file itkFEMElementBase.h.

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

Definition at line 89 of file itkFEMElementBase.h.

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

Floating point type used in all Element classes.

Definition at line 83 of file itkFEMElementBase.h.

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.

Definition at line 120 of file itkFEMElementBase.h.

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.

Definition at line 119 of file itkFEMElementBase.h.

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

Class used to store the element stiffness matrix

Definition at line 101 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.

Definition at line 520 of file itkFEMElementBase.h.

typedef SmartPointer<Self> itk::fem::Element::Pointer

Definition at line 79 of file itkFEMElementBase.h.

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

Standard class typedefs.

Definition at line 77 of file itkFEMElementBase.h.

typedef FEMLightObject itk::fem::Element::Superclass

Definition at line 78 of file itkFEMElementBase.h.

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

Class to store the element load vector

Definition at line 106 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 134 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 397 of file itkFEMElementBase.h.

virtual std::vector<std::vector<int> > itk::fem::Element::GetEdgeIds ( void ) const

virtual

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

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

virtual

Compute the physical energy, U, of the deformation (e.g. stress / strain ).

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

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

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::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

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::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

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.

virtual Material::ConstPointer itk::fem::Element::GetMaterial ( void ) const

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

virtual void itk::fem::Element::GetMaterialMatrix ( MatrixType & D ) const

pure virtual

Compute the element material matrix.

Parameters

D	Reference to a matrix object

virtual const char* itk::fem::Element::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::fem::FEMLightObject.

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 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

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 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedom ( void ) const

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.

virtual unsigned int itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode ( void ) const

pure virtual

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.

Note: This function must be overriden in all derived classes.

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

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 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

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

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::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

Compute the strain displacement matrix at local point.

Parameters

B	Reference to a matrix object that will contain the result
shapeDgl	Matrix that contains derivatives of shape functions w.r.t. global coordinates.

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 = `nullptr`
	)		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	reference 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 = `nullptr`
	)		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::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 = `nullptr`
	)		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, itk::fem::Element2DC0QuadraticTriangular, and itk::fem::Element3DC0LinearTriangular.

virtual void itk::fem::Element::PopulateEdgeIds ( void )

pure virtual

Set the edge order and the points defining each edge

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

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

overrideprotectedvirtual

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.

virtual void itk::fem::Element::SetMaterial ( Material::ConstPointer )

virtual

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.

See Also: GetMaterial

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 >, itk::fem::ElementStd< 4, 2 >, and itk::fem::ElementStd< 3, 3 >.

virtual void itk::fem::Element::SetNode	(	unsigned int	n,
		Node::Pointer	node
	)

virtual

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 >.

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::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 = `nullptr`,
		const MatrixType *	pshapeD = `nullptr`
	)		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::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

const unsigned int itk::fem::Element::gaussMaxOrder = 10

static

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

Definition at line 489 of file itkFEMElementBase.h.

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 502 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 509 of file itkFEMElementBase.h.

std::vector<std::vector<int> > itk::fem::Element::m_EdgeIds

protected

Definition at line 689 of file itkFEMElementBase.h.

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

itkFEMElementBase.h

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