#include <itkFEMElement2DC0QuadraticTriangular.h>

Inheritance diagram for itk::fem::Element2DC0QuadraticTriangular:

Collaboration diagram for itk::fem::Element2DC0QuadraticTriangular:

Detailed Description

6-noded, quadratic, C0 continuous finite element in 2D space that defines a triangle.

The ordering of the nodes is counter clockwise. That is the nodes should be defined in the following order:

(0,0.5) 5 * * 4 (0.5, 0.5) | \ | \ *--—*--—* 0 3 1 (0,0) (0,0.5) (0,1)

This class defines the geometry of the FE problem. It must be combined with the physics component of the problem. This has already been done in the following classes:

See Also: Element2DC0QuadraticTriangularStrain; Element2DC0QuadraticTriangularStress

Definition at line 58 of file itkFEMElement2DC0QuadraticTriangular.h.

Public Types
enum	{ DefaultIntegrationOrder = 2 }

typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Element2DC0QuadraticTriangular	Self

typedef TemplatedParentClass	Superclass

typedef ElementStd< 6, 2 >	TemplatedParentClass

Public Types inherited from itk::fem::ElementStd< 6, 2 >
enum

enum

enum

typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DegreeOfFreedomIDType	DegreeOfFreedomIDType

typedef Superclass::Float	Float

typedef Superclass::LoadPointer	LoadPointer

typedef Superclass::LoadType	LoadType

typedef Superclass::MatrixType	MatrixType

typedef Superclass::Node	Node

typedef Superclass::NodeIDType	NodeIDType

typedef SmartPointer< Self >	Pointer

typedef ElementStd	Self

typedef Element	Superclass

typedef Superclass::VectorType	VectorType

Public Types inherited from itk::fem::Element
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 void	GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order) const override

virtual bool	GetLocalFromGlobalCoordinates (const VectorType &GlobalPt, VectorType &LocalPt) const override

virtual const char *	GetNameOfClass () const

virtual unsigned int	GetNumberOfIntegrationPoints (unsigned int order) const override

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

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

virtual void	ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const override

virtual VectorType	ShapeFunctions (const VectorType &pt) const override

Public Member Functions inherited from itk::fem::ElementStd< 6, 2 >
	ElementStd ()

virtual const VectorType &	GetNodeCoordinates (unsigned int n) const override

virtual unsigned int	GetNumberOfNodes (void) const override

virtual unsigned int	GetNumberOfSpatialDimensions () const override

virtual void	SetNode (unsigned int n, NodeIDType node) override

virtual void	SetNode (unsigned int n, typename Superclass::Node::Pointer node) override

virtual NodeIDType	GetNode (unsigned int n) const override

Public Member Functions inherited from itk::fem::Element
virtual std::vector < std::vector< int > >	GetEdgeIds (void) const

virtual Float	GetElementDeformationEnergy (MatrixType &LocalSolution) const

virtual VectorType	GetGlobalFromLocalCoordinates (const VectorType &pt) const

virtual void	GetLandmarkContributionMatrix (float eta, MatrixType &Le) const

virtual void	GetMassMatrix (MatrixType &Me) const

virtual Material::ConstPointer	GetMaterial (void) const

virtual void	GetMaterialMatrix (MatrixType &D) const =0

virtual unsigned int	GetNumberOfDegreesOfFreedom (void) const

virtual unsigned int	GetNumberOfDegreesOfFreedomPerNode (void) 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 void	SetMaterial (Material::ConstPointer)

virtual void	ShapeFunctionGlobalDerivatives (const VectorType &pt, MatrixType &shapeDgl, const MatrixType pJ=nullptr, const MatrixType pshapeD=nullptr) const

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

Protected Member Functions
virtual void	PopulateEdgeIds (void) override

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

Protected Member Functions inherited from itk::fem::ElementStd< 6, 2 >
virtual void	SetNodeInternal (unsigned int n, const Node *node)

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 ()

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

static Pointer	New ()

Static Public Attributes inherited from itk::fem::Element
static const unsigned int	gaussMaxOrder = 10

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

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

Protected Attributes inherited from itk::fem::ElementStd< 6, 2 >
const Node *	m_node [NumberOfNodes]

Protected Attributes inherited from itk::fem::Element
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

Member Typedef Documentation

typedef SmartPointer<const Self> itk::fem::Element2DC0QuadraticTriangular::ConstPointer

Definition at line 67 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef SmartPointer<Self> itk::fem::Element2DC0QuadraticTriangular::Pointer

Definition at line 66 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef Element2DC0QuadraticTriangular itk::fem::Element2DC0QuadraticTriangular::Self

Standard class typedefs.

Definition at line 63 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef TemplatedParentClass itk::fem::Element2DC0QuadraticTriangular::Superclass

Definition at line 65 of file itkFEMElement2DC0QuadraticTriangular.h.

typedef ElementStd<6, 2> itk::fem::Element2DC0QuadraticTriangular::TemplatedParentClass

Definition at line 64 of file itkFEMElement2DC0QuadraticTriangular.h.

Member Enumeration Documentation

anonymous enum

Methods related to numeric integration

Enumerator
DefaultIntegrationOrder

Definition at line 77 of file itkFEMElement2DC0QuadraticTriangular.h.

Member Function Documentation

virtual void itk::fem::Element2DC0QuadraticTriangular::GetIntegrationPointAndWeight	(	unsigned int	i,
		VectorType &	pt,
		Float &	w,
		unsigned int	order
	)		const

overridevirtual

Get the Integration point and weight

Implements itk::fem::Element.

virtual bool itk::fem::Element2DC0QuadraticTriangular::GetLocalFromGlobalCoordinates	(	const VectorType &	GlobalPt,
		VectorType &	LocalPt
	)		const

overridevirtual

Convert from global to local coordinates

Implements itk::fem::Element.

virtual const char* itk::fem::Element2DC0QuadraticTriangular::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::fem::ElementStd< 6, 2 >.

Reimplemented in itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, and itk::fem::Element2DStress< Element2DC0QuadraticTriangular >.

virtual unsigned int itk::fem::Element2DC0QuadraticTriangular::GetNumberOfIntegrationPoints ( unsigned int order ) const

overridevirtual

Get the number of integration points

Implements itk::fem::Element.

virtual Float itk::fem::Element2DC0QuadraticTriangular::JacobianDeterminant	(	const VectorType &	pt,
		const MatrixType *	pJ = `nullptr`
	)		const

overridevirtual

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 from itk::fem::Element.

virtual void itk::fem::Element2DC0QuadraticTriangular::JacobianInverse	(	const VectorType &	pt,
		MatrixType &	invJ,
		const MatrixType *	pJ = `nullptr`
	)		const

overridevirtual

Compute the inverse of the Jacobian matrix

Reimplemented from itk::fem::Element.

virtual void itk::fem::Element2DC0QuadraticTriangular::PopulateEdgeIds ( void )

overrideprotectedvirtual

Set the edge order and the points defining each edge

Implements itk::fem::Element.

virtual void itk::fem::Element2DC0QuadraticTriangular::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::ElementStd< 6, 2 >.

Reimplemented in itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DC0QuadraticTriangularStrain, and itk::fem::Element2DC0QuadraticTriangularStress.