ITK
4.3.0
Insight Segmentation and Registration Toolkit
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#include <itkFEMElementBase.h>
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.
Definition at line 72 of file itkFEMElementBase.h.
Classes | |
class | Node |
Class that stores information required to define a node. More... | |
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=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 | 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=0, const MatrixType *pshapeD=0) 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 |
Static Public Attributes | |
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 |
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 () |
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 | |
InternalReferenceCountType | m_ReferenceCount |
SimpleFastMutexLock | m_ReferenceCountLock |
Additional Inherited Members | |
Static Public Member Functions inherited from itk::LightObject | |
static void | BreakOnError () |
static Pointer | New () |
Protected Types inherited from itk::LightObject | |
typedef int | InternalReferenceCountType |
typedef FEMPArray<Element> itk::fem::Element::ArrayType |
Array class that holds special pointers to the Element objects
Definition at line 94 of file itkFEMElementBase.h.
Definition at line 95 of file itkFEMElementBase.h.
typedef SmartPointer<const Self> itk::fem::Element::ConstPointer |
Definition at line 79 of file itkFEMElementBase.h.
typedef unsigned int itk::fem::Element::DegreeOfFreedomIDType |
Type that stores global ID's of degrees of freedom.
Definition at line 126 of file itkFEMElementBase.h.
typedef unsigned long itk::fem::Element::ElementIdentifier |
Definition at line 88 of file itkFEMElementBase.h.
typedef double itk::fem::Element::Float |
Floating point type used in all Element classes.
Definition at line 82 of file itkFEMElementBase.h.
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.
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 118 of file itkFEMElementBase.h.
typedef vnl_matrix<Float> itk::fem::Element::MatrixType |
Class used to store the element stiffness matrix
Definition at line 100 of file itkFEMElementBase.h.
Type that is used to store IDs of a node. It is a pointer to Node objects.
Definition at line 548 of file itkFEMElementBase.h.
typedef SmartPointer<Self> itk::fem::Element::Pointer |
Definition at line 78 of file itkFEMElementBase.h.
typedef Element itk::fem::Element::Self |
Standard class typedefs.
Definition at line 76 of file itkFEMElementBase.h.
Definition at line 77 of file itkFEMElementBase.h.
typedef vnl_vector<Float> itk::fem::Element::VectorType |
Class to store the element load vector
Definition at line 105 of file itkFEMElementBase.h.
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.
Definition at line 133 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.
Definition at line 517 of file itkFEMElementBase.h.
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Convenient way to access IDs of degrees of freedom that are stored in node objects.
local_dof | Local number of degree of freedom within an element. |
Definition at line 420 of file itkFEMElementBase.h.
References GetNode(), GetNumberOfDegreesOfFreedom(), GetNumberOfDegreesOfFreedomPerNode(), and InvalidDegreeOfFreedomID.
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Access the edge ids vector. The vector in turn contains a list of edge ids.
Definition at line 706 of file itkFEMElementBase.h.
References m_EdgeIds.
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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.
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Transforms the given local element coordinates into global.
pt | Point in local element coordinates. |
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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.
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. |
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.
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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.
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Transforms the given global element coordinates into local. Returns false if the point is outside.
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.
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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.
Reimplemented in itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element2DC1Beam, and itk::fem::Element2DC0LinearLineStress.
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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.
Reimplemented in itk::fem::Element2DC1Beam, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
Definition at line 448 of file itkFEMElementBase.h.
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Compute the element material matrix.
D | Reference to a matrix object |
Implemented in itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DC1Beam, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, and itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >.
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Run-time type information (and related methods).
Reimplemented from itk::fem::FEMLightObject.
Reimplemented in itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element2DC0LinearQuadrilateral, 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 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element3DC0LinearTriangularMembrane, itk::fem::Element2DC1Beam, itk::fem::Element2DC0LinearLineStress, and itk::fem::Element2DC0LinearLine.
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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 >.
Referenced by GetDegreeOfFreedom().
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Return a vector of global coordinates of n-th node in an element.
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 >.
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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 698 of file itkFEMElementBase.h.
References GetNumberOfDegreesOfFreedomPerNode(), and GetNumberOfNodes().
Referenced by GetDegreeOfFreedom().
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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.
Implemented in itk::fem::Element2DC1Beam, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, and itk::fem::Element3DC0LinearTriangularLaplaceBeltrami.
Referenced by GetDegreeOfFreedom(), and GetNumberOfDegreesOfFreedom().
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Returns total number of integration points, for given order of Gauss-Legendre numerical integration rule.
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.
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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 >.
Referenced by GetNumberOfDegreesOfFreedom().
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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 >.
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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.
Ke | Reference to the resulting stiffnes matrix. |
Reimplemented in itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, and itk::fem::Element2DC1Beam.
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Compute the strain displacement matrix at local point.
B | Reference to a matrix object that will contain the result |
shapeDgl | Matrix that contains derivatives of shape functions w.r.t. global coordinates. |
Implemented in itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DC1Beam, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, and itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >.
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Return interpolated value of all unknown functions at given local point.
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. |
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Return interpolated value of f-th unknown function at given local point.
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. |
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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.
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.
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Compute the determinant of the Jacobian matrix at a given point with respect to the local coordinate system.
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.
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Compute the inverse of the Jacobian matrix at a given point with respect to the local coordinate system.
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.
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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.
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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.
Reimplemented in itk::fem::Element2DC1Beam, 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 >, itk::fem::ElementStd< 3, 3 >, itk::fem::Element3DC0LinearTriangular, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element2DC0LinearTriangular, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element3DC0LinearHexahedron, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >, itk::fem::Element2DC0LinearQuadrilateral, itk::fem::Element2DC0QuadraticTriangular, itk::fem::Element3DC0LinearTetrahedron, itk::fem::Element2DC0LinearLine, itk::fem::Element2DC0QuadraticTriangularStrain, itk::fem::Element2DC0QuadraticTriangularStress, itk::fem::Element2DC0LinearQuadrilateralMembrane, itk::fem::Element2DC0LinearQuadrilateralStress, itk::fem::Element2DC0LinearTriangularMembrane, itk::fem::Element2DC0LinearQuadrilateralStrain, itk::fem::Element2DC0LinearTriangularStrain, itk::fem::Element3DC0LinearTriangularLaplaceBeltrami, itk::fem::Element2DC0LinearTriangularStress, itk::fem::Element3DC0LinearHexahedronMembrane, itk::fem::Element3DC0LinearHexahedronStrain, itk::fem::Element3DC0LinearTetrahedronMembrane, itk::fem::Element3DC0LinearTetrahedronStrain, itk::fem::Element2DC0LinearLineStress, and itk::fem::Element3DC0LinearTriangularMembrane.
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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.
Reimplemented in itk::fem::Element2DC1Beam, itk::fem::Element2DMembrane< Element2DC0LinearQuadrilateral >, itk::fem::Element2DMembrane< Element2DC0LinearTriangular >, itk::fem::Element1DStress< Element2DC0LinearLine >, itk::fem::Element2DStrain< Element2DC0QuadraticTriangular >, itk::fem::Element2DStrain< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStrain< Element2DC0LinearTriangular >, itk::fem::Element3DMembrane< Element3DC0LinearHexahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTetrahedron >, itk::fem::Element3DMembrane< Element3DC0LinearTriangular >, itk::fem::Element3DMembrane1DOF< Element3DC0LinearTriangular >, itk::fem::Element2DStress< Element2DC0QuadraticTriangular >, itk::fem::Element2DStress< Element2DC0LinearQuadrilateral >, itk::fem::Element2DStress< Element2DC0LinearTriangular >, itk::fem::Element3DStrain< Element3DC0LinearHexahedron >, and itk::fem::Element3DStrain< Element3DC0LinearTetrahedron >.
Definition at line 461 of file itkFEMElementBase.h.
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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 >.
Referenced by SetNode().
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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 >.
Definition at line 564 of file itkFEMElementBase.h.
References itk::SmartPointer< TObjectType >::GetPointer(), and SetNode().
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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.
pt | Point in local element coordinates. |
shapeD | Reference to a matrix object, which will be filled with values of shape function derivatives. |
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.
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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.
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. |
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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.
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.
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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.
Definition at line 530 of file itkFEMElementBase.h.
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Weights for Gauss-Legendre integration.
Definition at line 537 of file itkFEMElementBase.h.
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Definition at line 726 of file itkFEMElementBase.h.
Referenced by GetEdgeIds().