itk::fem::Element2DC0LinearTriangularStrain Class Reference

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 125 of file itkFEMElementBase.h.

anonymous enum [inherited]

Maximum supported order of 1D Gauss-Legendre integration. Integration points are defined for orders from 1 to gaussMaxOrder. Number of integration points is equal to the order of integration rule.

See also:: gaussPoint

Enumerator:

gaussMaxOrder

Definition at line 473 of file itkFEMElementBase.h.

anonymous enum [inherited]

Definition at line 69 of file itkFEMElementStd.h.

anonymous enum [inherited]

Number of nodes that define the element.

Definition at line 74 of file itkFEMElementStd.h.

anonymous enum [inherited]

Number of dimensions of space in which element can exist.

Definition at line 79 of file itkFEMElementStd.h.

Constructor & Destructor Documentation

itk::fem::Element2DC0LinearTriangularStrain::Element2DC0LinearTriangularStrain ( )

Default constructor only clears the internal storage

itk::fem::Element2DC0LinearTriangularStrain::Element2DC0LinearTriangularStrain	(	NodeIDType	n1_,
		NodeIDType	n2_,
		NodeIDType	n3_,
		Material::ConstPointer	p_
	)

Construct an element by specifying pointers to 3 points and a material.

Member Function Documentation

virtual int itk::fem::Element2DC0LinearTriangularStrain::ClassID ( ) const [inline, virtual]

Virtual function to access the class ID

Implements itk::fem::FEMLightObject.

Definition at line 35 of file itkFEMElement2DC0LinearTriangularStrain.h.

virtual Baseclass::Pointer itk::fem::Element2DC0LinearTriangularStrain::Clone ( ) const [virtual]

Create a new object from the existing one

Implements itk::fem::FEMLightObject.

static FEMLightObject::Pointer itk::fem::FEMLightObject::CreateFromStream	(	std::istream &	f,
		void *	info
	)			`[static, inherited]`

Read object of any derived type from stream.

This static function creates an object of a class, which is derived from FEMLightObject. The class of object is first determined from the stream, then the object of that class is constructed using the FEMObjectFactory. Finally the data for this object is read from the stream, by calling the Read() member function.

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

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

Parameters:

local_dof

Local number of degree of freedom within an element.

Definition at line 389 of file itkFEMElementBase.h.

References itk::fem::Element::Element::Node::GetDegreeOfFreedom(), itk::fem::Element::GetNode(), itk::fem::Element::GetNumberOfDegreesOfFreedom(), itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode(), and itk::fem::Element::InvalidDegreeOfFreedomID.

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

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

T U = u Ke u

The matrix LocalSolution contains the solution to use in the energy computation. Usually, this is the solution at the nodes.

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

Transforms the given local element coordinates into global.

Parameters:

pt

Point in local element coordinates.

virtual void itk::fem::Element2DC0LinearTriangular::GetIntegrationPointAndWeight	(	unsigned int	i,
		VectorType &	pt,
		Float &	w,
		unsigned int	order
	)			const `[virtual, inherited]`

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()

Implements itk::fem::Element.

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

Compute and return landmark contribution to element stiffness matrix (Le) in global coordinate system.

b T int (1/eta)^2 N(x) N(x) dx a

where (eta ) is the landmark weight. Implementation is similar to GetMassMatrix.

virtual void itk::fem::Element::GetLoadVector	(	LoadPointer	l,
		VectorType &	Fe
	)			const `[pure virtual, inherited]`

Compute and return the element load vector for a given external load. The class of load object determines the type of load acting on the elemnent. Basically this is the contribution of this element on the right side of the master matrix equation, due to the specified load. Returned vector includes only nodal forces that correspond to the given Load object.

Visitor design pattern is used in the loads implementation. This function only selects and calls the proper function based on the given class of load object. The code that performs the actual conversion to the corresponding nodal loads is defined elswhere.

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::Element2DC0LinearTriangular::GetLocalFromGlobalCoordinates	(	const VectorType &	globalPt,
		VectorType &	localPt
	)			const `[virtual, inherited]`

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.

Implements itk::fem::Element.

void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::GetMassMatrix ( MatrixType & Me ) const [virtual, inherited]

Compute the mass matrix specific for 2D strain problems.

Reimplemented from itk::fem::Element.

virtual Material::ConstPointer itk::fem::Element2DStrain< Element2DC0LinearTriangular >::GetMaterial ( void ) const [inline, virtual, inherited]

Pointer to material properties of the element

Reimplemented from itk::fem::Element.

Definition at line 100 of file itkFEMElement2DStrain.h.

virtual void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::GetMaterialMatrix ( MatrixType & D ) const [virtual, inherited]

Compute the D matrix.

Implements itk::fem::Element.

virtual NodeIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNode ( unsigned int n ) const [inline, virtual, inherited]

Implements itk::fem::Element.

Definition at line 93 of file itkFEMElementStd.h.

virtual const VectorType& itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNodeCoordinates ( unsigned int n ) const [inline, virtual, inherited]

Implements itk::fem::Element.

Definition at line 111 of file itkFEMElementStd.h.

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

Return the total number of degrees of freedom defined in a derived element class. By default this is equal to number of points in a cell multiplied by number of degrees of freedom at each point.

Definition at line 650 of file itkFEMElementBase.h.

References itk::fem::Element::GetNumberOfDegreesOfFreedomPerNode(), and itk::fem::Element::GetNumberOfNodes().

Referenced by itk::fem::Element::GetDegreeOfFreedom().

virtual unsigned int itk::fem::Element2DStrain< Element2DC0LinearTriangular >::GetNumberOfDegreesOfFreedomPerNode ( void ) const [inline, virtual, inherited]

2D strain elements have 2 DOFs per node.

Implements itk::fem::Element.

Definition at line 91 of file itkFEMElement2DStrain.h.

virtual unsigned int itk::fem::Element2DC0LinearTriangular::GetNumberOfIntegrationPoints ( unsigned int order ) const [virtual, inherited]

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()

Implements itk::fem::Element.

virtual unsigned int itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNumberOfNodes ( void ) const [inline, virtual, inherited]

Methods that define the geometry of an element

Implements itk::fem::Element.

Definition at line 90 of file itkFEMElementStd.h.

virtual unsigned int itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::GetNumberOfSpatialDimensions ( ) const [inline, virtual, inherited]

Implements itk::fem::Element.

Definition at line 116 of file itkFEMElementStd.h.

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

Compute and return element stiffnes matrix (Ke) in global coordinate system. The base class provides a general implementation which only computes

b T int B(x) D B(x) dx a

using the Gaussian numeric integration method. The function calls GetIntegrationPointAndWeight() / GetNumberOfIntegrationPoints() to obtain the integration points. It also calls the GetStrainDisplacementMatrix() and GetMaterialMatrix() member functions.

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 void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::GetStrainDisplacementMatrix	(	MatrixType &	B,
		const MatrixType &	shapeDgl
	)			const `[virtual, inherited]`

Methods related to the physics of the problem. Compute the B matrix.

Implements itk::fem::Element.

virtual VectorType itk::fem::Element::GetStrainsAtPoint	(	const VectorType &	pt,
		const Solution &	sol,
		unsigned int	index
	)			const `[virtual, inherited]`

virtual VectorType itk::fem::Element::GetStressesAtPoint	(	const VectorType &	pt,
		const VectorType &	e,
		const Solution &	sol,
		unsigned int	index
	)			const `[virtual, inherited]`

itk::fem::Element2DC0LinearTriangularStrain::HANDLE_ELEMENT_LOADS ( )

virtual VectorType itk::fem::Element::InterpolateSolution	(	const VectorType &	pt,
		const Solution &	sol,
		unsigned int	solutionIndex = `0`
	)			const `[virtual, inherited]`

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

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, inherited]`

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, inherited]`

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::Element2DC0LinearTriangular::JacobianDeterminant	(	const VectorType &	pt,
		const MatrixType *	pJ = `0`
	)			const `[virtual, inherited]`

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

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::Element2DC0LinearTriangular::JacobianInverse	(	const VectorType &	pt,
		MatrixType &	invJ,
		const MatrixType *	pJ = `0`
	)			const `[virtual, inherited]`

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

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 from itk::fem::Element.

static Self::Pointer itk::fem::Element2DC0LinearTriangularStrain::New ( void ) [inline, static]

Object creation in an itk compatible way

Definition at line 35 of file itkFEMElement2DC0LinearTriangularStrain.h.

virtual void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::Read	(	std::istream &	,
		void *	info
	)			`[virtual, inherited]`

Read data for this class from input stream

Reimplemented from itk::fem::ElementStd< 3, 2 >.

virtual void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::SetMaterial ( Material::ConstPointer mat_ ) [inline, virtual, inherited]

Pointer to material properties of the element

Reimplemented from itk::fem::Element.

Definition at line 101 of file itkFEMElement2DStrain.h.

virtual void itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::SetNode	(	unsigned int	n,
		NodeIDType	node
	)			`[inline, virtual, inherited]`

Implements itk::fem::Element.

Definition at line 102 of file itkFEMElementStd.h.

virtual void itk::fem::Element2DC0LinearTriangular::ShapeFunctionDerivatives	(	const VectorType &	pt,
		MatrixType &	shapeD
	)			const `[virtual, inherited]`

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

Implements itk::fem::Element.

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

Compute matrix of shape function derivatives with respect to global coordinates.

A column in this matrix corresponds to a specific shape function, while a row corresponds to different global coordinates.

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::Element2DC0LinearTriangular::ShapeFunctions ( const VectorType & pt ) const [virtual, inherited]

Methods related to the geometry of an element

Implements itk::fem::Element.

static void itk::fem::FEMLightObject::SkipWhiteSpace ( std::istream & f ) [static, inherited]

Helper function that skips all the whitespace and comments in an input stream.

virtual void itk::fem::Element2DStrain< Element2DC0LinearTriangular >::Write ( std::ostream & f ) const [virtual, inherited]

Write this class to output stream

Reimplemented from itk::fem::ElementStd< 3, 2 >.

Member Data Documentation

const int itk::fem::Element2DC0LinearTriangularStrain::CLID [static]

Class ID for FEM object factory

Definition at line 35 of file itkFEMElement2DC0LinearTriangularStrain.h.

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

Points for 1D Gauss-Legendre integration from -1 to 1. First index is order of integration, second index is the number of integration point.

Example: gaussPoint[4][2] returns third point of the 4th order integration rule. Subarray gaussPoint[0][...] does not provide useful information. It is there only to keep order index correct.

See also:: gaussWeight

Definition at line 486 of file itkFEMElementBase.h.

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

Weights for Gauss-Legendre integration.

See also:: gaussPoint

Definition at line 493 of file itkFEMElementBase.h.

int itk::fem::FEMLightObject::GN [inherited]

Global number of an object (ID of an object) In general the ID's are required to be unique only within a specific type of derived classes (Elements, Nodes, ...) If the GN is not required, it can be ignored. (normally you need the GN when writing or reading objects to/from stream.

Definition at line 165 of file itkFEMLightObject.h.

Referenced by itk::fem::FEMLightObject::FEMLightObject().

MaterialLinearElasticity::ConstPointer itk::fem::Element2DStrain< Element2DC0LinearTriangular >::m_mat [inherited]

Pointer to material properties of the element

Definition at line 99 of file itkFEMElement2DStrain.h.

NodeIDType itk::fem::ElementStd< VNumberOfNodes, VNumberOfSpatialDimensions, Element >::m_node[NumberOfNodes] [protected, inherited]

Array of pointers to point objects that define the element

Definition at line 141 of file itkFEMElementStd.h.

const unsigned int itk::fem::Element2DC0LinearTriangular::Nip[6] [static, inherited]

Array that holds number of integration point for each order of numerical integration.

Definition at line 81 of file itkFEMElement2DC0LinearTriangular.h.

const Float itk::fem::Element2DC0LinearTriangular::trigGaussRuleInfo[6][7][4] [static, inherited]

Draw the element on the specified device context Constants for integration rules.

Definition at line 75 of file itkFEMElement2DC0LinearTriangular.h.

const std::string itk::fem::FEMLightObject::whitespaces [static, inherited]

Const string of all whitespace characters. This string is used by SkipWhiteSpace function.

Definition at line 135 of file itkFEMLightObject.h.

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

itkFEMElement2DC0LinearTriangularStrain.h


Public Types
enum	{ DefaultIntegrationOrder = 1 }
enum	{ InvalidDegreeOfFreedomID = 0xffffffff }
enum	{ gaussMaxOrder = 10 }
enum
enum
enum
typedef FEMPArray< Element >	ArrayType
typedef Self	Baseclass
typedef const Self *	ConstPointer
Public Member Functions
virtual int	ClassID () const
virtual Baseclass::Pointer	Clone () const
	Element2DC0LinearTriangularStrain (NodeIDType n1_, NodeIDType n2_, NodeIDType n3_, Material::ConstPointer p_)
	Element2DC0LinearTriangularStrain ()
virtual Float	GetElementDeformationEnergy (MatrixType &LocalSolution) const
virtual VectorType	GetGlobalFromLocalCoordinates (const VectorType &pt) const
virtual void	GetIntegrationPointAndWeight (unsigned int i, VectorType &pt, Float &w, unsigned int order) const
virtual void	GetLandmarkContributionMatrix (float eta, MatrixType &Le) const
virtual void	GetLoadVector (LoadPointer l, VectorType &Fe) const =0
virtual bool	GetLocalFromGlobalCoordinates (const VectorType &globalPt, VectorType &localPt) const
void	GetMassMatrix (MatrixType &Me) const
virtual void	GetMaterialMatrix (MatrixType &D) const
virtual NodeIDType	GetNode (unsigned int n) const
virtual const VectorType &	GetNodeCoordinates (unsigned int n) const
virtual unsigned int	GetNumberOfDegreesOfFreedom (void) const
virtual unsigned int	GetNumberOfDegreesOfFreedomPerNode (void) const
virtual unsigned int	GetNumberOfIntegrationPoints (unsigned int order) const
virtual unsigned int	GetNumberOfNodes (void) const
virtual unsigned int	GetNumberOfSpatialDimensions () const
virtual void	GetStiffnessMatrix (MatrixType &Ke) const
virtual void	GetStrainDisplacementMatrix (MatrixType &B, const MatrixType &shapeDgl) const
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
	HANDLE_ELEMENT_LOADS ()
virtual VectorType	InterpolateSolution (const VectorType &pt, const Solution &sol, unsigned int solutionIndex=0) const
virtual Float	InterpolateSolutionN (const VectorType &pt, const Solution &sol, unsigned int f, unsigned int solutionIndex=0) const
virtual void	Jacobian (const VectorType &pt, MatrixType &J, const MatrixType *pshapeD=0) const
virtual Float	JacobianDeterminant (const VectorType &pt, const MatrixType *pJ=0) const
virtual void	JacobianInverse (const VectorType &pt, MatrixType &invJ, const MatrixType *pJ=0) const
virtual void	Read (std::istream &, void *info)
virtual void	SetNode (unsigned int n, NodeIDType node)
virtual void	ShapeFunctionDerivatives (const VectorType &pt, MatrixType &shapeD) const
virtual void	ShapeFunctionGlobalDerivatives (const VectorType &pt, MatrixType &shapeDgl, const MatrixType pJ=0, const MatrixType pshapeD=0) const
virtual VectorType	ShapeFunctions (const VectorType &pt) const
virtual void	Write (std::ostream &f) const

DegreeOfFreedomIDType	GetDegreeOfFreedom (unsigned int local_dof) const
Static Public Member Functions
static FEMLightObject::Pointer	CreateFromStream (std::istream &f, void *info)
static Self::Pointer	New ()
static void	SkipWhiteSpace (std::istream &f)
Public Attributes
int	GN
Static Public Attributes
static const int	CLID
static const Float	gaussPoint [gaussMaxOrder+1][gaussMaxOrder]
static const Float	gaussWeight [gaussMaxOrder+1][gaussMaxOrder]
static const unsigned int	Nip [6]
static const Float	trigGaussRuleInfo [6][7][4]
static const std::string	whitespaces
Protected Attributes
NodeIDType	m_node [NumberOfNodes]
virtual Material::ConstPointer	GetMaterial (void) const
virtual void	SetMaterial (Material::ConstPointer mat_)
MaterialLinearElasticity::ConstPointer	m_mat