ITK  4.8.0
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itk::fem::Element2DC0QuadraticTriangular Class Reference

#include <itkFEMElement2DC0QuadraticTriangular.h>

+ Inheritance diagram for itk::fem::Element2DC0QuadraticTriangular:
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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:

     (0,1)
     2
     *
     |\
     |  \
     |    \

(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 SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
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 SelfConstPointer
 
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< SelfPointer
 
typedef ElementStd Self
 
typedef Element Superclass
 
typedef Superclass::VectorType VectorType
 
- Public Types inherited from itk::fem::Element
enum  { InvalidDegreeOfFreedomID = 0xffffffff }
 
enum  { gaussMaxOrder = 10 }
 
typedef FEMPArray< ElementArrayType
 
typedef VectorContainer
< ElementIdentifier,
Element::Pointer
ArrayType1
 
typedef SmartPointer< const SelfConstPointer
 
typedef unsigned int DegreeOfFreedomIDType
 
typedef unsigned long ElementIdentifier
 
typedef double Float
 
typedef vnl_matrix< FloatMatrixType
 
typedef Node::ConstPointer NodeIDType
 
typedef SmartPointer< SelfPointer
 
typedef Element Self
 
typedef FEMLightObject Superclass
 
typedef vnl_vector< FloatVectorType
 
typedef FEMLightObject LoadType
 
typedef LoadType::Pointer LoadPointer
 
- Public Types inherited from itk::fem::FEMLightObject
typedef Self Baseclass
 
typedef SmartPointer< const SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
typedef FEMLightObject Self
 
typedef itk::LightObject Superclass
 
- Public Types inherited from itk::LightObject
typedef SmartPointer< const SelfConstPointer
 
typedef SmartPointer< SelfPointer
 
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 NodeIDType GetNode (unsigned int n) const override
 
virtual const VectorTypeGetNodeCoordinates (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
 
- 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 ()
 
- 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 Float gaussPoint [gaussMaxOrder+1][gaussMaxOrder]
 
static const Float gaussWeight [gaussMaxOrder+1][gaussMaxOrder]
 
- Protected Attributes inherited from itk::fem::ElementStd< 6, 2 >
const Nodem_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

Definition at line 67 of file itkFEMElement2DC0QuadraticTriangular.h.

Definition at line 66 of file itkFEMElement2DC0QuadraticTriangular.h.

Standard class typedefs.

Definition at line 63 of file itkFEMElement2DC0QuadraticTriangular.h.

Definition at line 65 of file itkFEMElement2DC0QuadraticTriangular.h.

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
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
ptPoint in local element coordinates.
pJOptional pointer to Jacobian matrix computed at point pt. If this is set to 0, the Jacobian will be computed as necessary.

Reimplemented 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.

virtual void itk::fem::Element2DC0QuadraticTriangular::ShapeFunctionDerivatives ( const VectorType pt,
MatrixType shapeD 
) const
overridevirtual

Return the shape functions derivatives in the shapeD matrix

Implements itk::fem::Element.

virtual VectorType itk::fem::Element2DC0QuadraticTriangular::ShapeFunctions ( const VectorType pt) const
overridevirtual

Methods related to the geometry of an elementReturn the shape functions used to interpolate across the element

Implements itk::fem::Element.


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