KratosMultiphysics
KRATOS Multiphysics (Kratos) is a framework for building parallel, multi-disciplinary simulation software, aiming at modularity, extensibility, and high performance. Kratos is written in C++, and counts with an extensive Python interface.
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Kratos::Triangle2D15< TPointType > Class Template Reference

A fifteen node 2D triangular geometry with quartic shape functions. More...

#include <triangle_2d_15.h>

Inheritance diagram for Kratos::Triangle2D15< TPointType >:
Collaboration diagram for Kratos::Triangle2D15< TPointType >:

Public Member Functions

Life Cycle
 Triangle2D15 (const PointType &Point01, const PointType &Point02, const PointType &Point03, const PointType &Point04, const PointType &Point05, const PointType &Point06, const PointType &Point07, const PointType &Point08, const PointType &Point09, const PointType &Point10, const PointType &Point11, const PointType &Point12, const PointType &Point13, const PointType &Point14, const PointType &Point15)
 
 Triangle2D15 (typename PointType::Pointer pPoint01, typename PointType::Pointer pPoint02, typename PointType::Pointer pPoint03, typename PointType::Pointer pPoint04, typename PointType::Pointer pPoint05, typename PointType::Pointer pPoint06, typename PointType::Pointer pPoint07, typename PointType::Pointer pPoint08, typename PointType::Pointer pPoint09, typename PointType::Pointer pPoint10, typename PointType::Pointer pPoint11, typename PointType::Pointer pPoint12, typename PointType::Pointer pPoint13, typename PointType::Pointer pPoint14, typename PointType::Pointer pPoint15)
 
 Triangle2D15 (const PointsArrayType &ThisPoints)
 
 Triangle2D15 (const IndexType GeometryId, const PointsArrayType &rThisPoints)
 Constructor with Geometry Id. More...
 
 Triangle2D15 (const std::string &rGeometryName, const PointsArrayType &rThisPoints)
 Constructor with Geometry Name. More...
 
 Triangle2D15 (Triangle2D15 const &rOther)
 
template<class TOtherPointType >
 Triangle2D15 (Triangle2D15< TOtherPointType > const &rOther)
 
 ~Triangle2D15 () override
 
GeometryData::KratosGeometryFamily GetGeometryFamily () const override
 
GeometryData::KratosGeometryType GetGeometryType () const override
 
Operators
Triangle2D15operator= (const Triangle2D15 &rOther)
 
template<class TOtherPointType >
Triangle2D15operator= (Triangle2D15< TOtherPointType > const &rOther)
 
Operations
BaseType::Pointer Create (PointsArrayType const &rThisPoints) const override
 Creates a new geometry pointer. More...
 
BaseType::Pointer Create (const IndexType NewGeometryId, PointsArrayType const &rThisPoints) const override
 Creates a new geometry pointer. More...
 
BaseType::Pointer Create (const BaseType &rGeometry) const override
 Creates a new geometry pointer. More...
 
BaseType::Pointer Create (const IndexType NewGeometryId, const BaseType &rGeometry) const override
 Creates a new geometry pointer. More...
 
MatrixPointsLocalCoordinates (Matrix &rResult) const override
 
Information
double Length () const override
 
double Area () const override
 
double DomainSize () const override
 
bool IsInside (const CoordinatesArrayType &rPoint, CoordinatesArrayType &rResult, const double Tolerance=std::numeric_limits< double >::epsilon()) const override
 Returns whether given arbitrary point is inside the Geometry and the respective local point for the given global point. More...
 
Shape Function
VectorShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType &rCoordinates) const override
 Returns vector of shape function values at local coordinate. More...
 
double ShapeFunctionValue (IndexType ShapeFunctionIndex, const CoordinatesArrayType &rPoint) const override
 
Input and output
std::string Info () const override
 
void PrintInfo (std::ostream &rOStream) const override
 
void PrintData (std::ostream &rOStream) const override
 
Edge
SizeType EdgesNumber () const override
 This method gives you number of all edges of this geometry. More...
 
GeometriesArrayType GenerateEdges () const override
 This method gives you all edges of this geometry. More...
 
SizeType FacesNumber () const override
 Returns the number of faces of the current geometry. More...
 
void NumberNodesInFaces (DenseVector< unsigned int > &NumberNodesInFaces) const override
 
void NodesInFaces (DenseMatrix< unsigned int > &NodesInFaces) const override
 
virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients (IntegrationMethod ThisMethod)
 
virtual ShapeFunctionsGradientsType ShapeFunctionsLocalGradients ()
 
MatrixShapeFunctionsLocalGradients (Matrix &rResult, const CoordinatesArrayType &rPoint) const override
 
virtual MatrixShapeFunctionsGradients (Matrix &rResult, const CoordinatesArrayType &rPoint)
 
ShapeFunctionsSecondDerivativesTypeShapeFunctionsSecondDerivatives (ShapeFunctionsSecondDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override
 
ShapeFunctionsThirdDerivativesTypeShapeFunctionsThirdDerivatives (ShapeFunctionsThirdDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override
 
- Public Member Functions inherited from Kratos::Geometry< TPointType >
 Geometry ()
 Standard Constructor. Generates self assigned id. More...
 
 Geometry (IndexType GeomertyId)
 Standard Constructor with a geometry Id. More...
 
 Geometry (const std::string &GeometryName)
 Standard Constructor with a Name. More...
 
 Geometry (const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())
 
 Geometry (IndexType GeometryId, const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())
 
 Geometry (const std::string &GeometryName, const PointsArrayType &ThisPoints, GeometryData const *pThisGeometryData=&GeometryDataInstance())
 
 Geometry (const Geometry &rOther)
 Copy constructor. More...
 
template<class TOtherPointType >
 Geometry (Geometry< TOtherPointType > const &rOther)
 Copy constructor with TOtherPointType. More...
 
virtual ~Geometry ()
 Destructor. Do nothing!!! More...
 
Geometryoperator= (const Geometry &rOther)
 
template<class TOtherPointType >
Geometryoperator= (Geometry< TOtherPointType > const &rOther)
 
 operator PointsArrayType & ()
 
TPointType & operator[] (const SizeType &i)
 
TPointType const & operator[] (const SizeType &i) const
 
PointPointerTypeoperator() (const SizeType &i)
 
ConstPointPointerTypeoperator() (const SizeType &i) const
 
iterator begin ()
 
const_iterator begin () const
 
iterator end ()
 
const_iterator end () const
 
ptr_iterator ptr_begin ()
 
ptr_const_iterator ptr_begin () const
 
ptr_iterator ptr_end ()
 
ptr_const_iterator ptr_end () const
 
PointReferenceType front ()
 
ConstPointReferenceType front () const
 
PointReferenceType back ()
 
ConstPointReferenceType back () const
 
SizeType size () const
 
SizeType PointsNumber () const
 
virtual SizeType PointsNumberInDirection (IndexType LocalDirectionIndex) const
 Returns number of points per direction. More...
 
SizeType max_size () const
 
void swap (GeometryType &rOther)
 
void push_back (PointPointerType x)
 
void clear ()
 
void reserve (int dim)
 
int capacity ()
 
PointPointerContainerTypeGetContainer ()
 ‍** Gives a reference to underly normal container. *‍/ More...
 
const PointPointerContainerTypeGetContainer () const
 
DataValueContainerGetData ()
 
DataValueContainer const & GetData () const
 
void SetData (DataValueContainer const &rThisData)
 
template<class TDataType >
bool Has (const Variable< TDataType > &rThisVariable) const
 
template<class TVariableType >
void SetValue (const TVariableType &rThisVariable, typename TVariableType::Type const &rValue)
 
template<class TVariableType >
TVariableType::Type & GetValue (const TVariableType &rThisVariable)
 
template<class TVariableType >
TVariableType::Type const & GetValue (const TVariableType &rThisVariable) const
 
virtual void Assign (const Variable< bool > &rVariable, const bool Input)
 Assign with bool. More...
 
virtual void Assign (const Variable< int > &rVariable, const int Input)
 Assign with int. More...
 
virtual void Assign (const Variable< double > &rVariable, const double Input)
 Assign with double. More...
 
virtual void Assign (const Variable< array_1d< double, 2 >> &rVariable, const array_1d< double, 2 > &rInput)
 Assign with array_1d<double, 2> More...
 
virtual void Assign (const Variable< array_1d< double, 3 >> &rVariable, const array_1d< double, 3 > &rInput)
 Assign with array_1d<double, 3> More...
 
virtual void Assign (const Variable< array_1d< double, 6 >> &rVariable, const array_1d< double, 6 > &rInput)
 Assign with array_1d<double, 6> More...
 
virtual void Assign (const Variable< Vector > &rVariable, const Vector &rInput)
 Assign with Vector. More...
 
virtual void Assign (const Variable< Matrix > &rVariable, const Matrix &rInput)
 Assign with Matrix. More...
 
virtual void Calculate (const Variable< bool > &rVariable, bool &rOutput) const
 Calculate with bool. More...
 
virtual void Calculate (const Variable< int > &rVariable, int &rOutput) const
 Calculate with int. More...
 
virtual void Calculate (const Variable< double > &rVariable, double &rOutput) const
 Calculate with double. More...
 
virtual void Calculate (const Variable< array_1d< double, 2 >> &rVariable, array_1d< double, 2 > &rOutput) const
 Calculate with array_1d<double, 2> More...
 
virtual void Calculate (const Variable< array_1d< double, 3 >> &rVariable, array_1d< double, 3 > &rOutput) const
 Calculate with array_1d<double, 3> More...
 
virtual void Calculate (const Variable< array_1d< double, 6 >> &rVariable, array_1d< double, 6 > &rOutput) const
 Calculate with array_1d<double, 6> More...
 
virtual void Calculate (const Variable< Vector > &rVariable, Vector &rOutput) const
 Calculate with Vector. More...
 
virtual void Calculate (const Variable< Matrix > &rVariable, Matrix &rOutput) const
 Calculate with Matrix. More...
 
Pointer Create (const std::string &rNewGeometryName, PointsArrayType const &rThisPoints) const
 Creates a new geometry pointer. More...
 
virtual Pointer Create (const GeometryType &rGeometry) const
 Creates a new geometry pointer. More...
 
virtual Pointer Create (const IndexType NewGeometryId, const GeometryType &rGeometry) const
 Creates a new geometry pointer. More...
 
Pointer Create (const std::string &rNewGeometryName, const GeometryType &rGeometry) const
 Creates a new geometry pointer. More...
 
void ClonePoints ()
 
virtual VectorLumpingFactors (Vector &rResult, const LumpingMethods LumpingMethod=LumpingMethods::ROW_SUM) const
 Lumping factors for the calculation of the lumped mass matrix. More...
 
GeometryData const & GetGeometryData () const
 GeometryData contains all information about dimensions and has a set of precomputed values for integration points and shape functions, including derivatives. More...
 
virtual void SetGeometryShapeFunctionContainer (const GeometryShapeFunctionContainer< GeometryData::IntegrationMethod > &rGeometryShapeFunctionContainer)
 
virtual GeometryTypeGetGeometryParent (IndexType Index) const
 Some geometries require relations to other geometries. This is the case for e.g. quadrature points. To reach the parent geometry this function can be used. More...
 
virtual void SetGeometryParent (GeometryType *pGeometryParent)
 Some geometries require relations to other geometries. This is the case for e.g. quadrature points. To set or change the parent geometry this function can be used. More...
 
virtual GeometryTypeGetGeometryPart (const IndexType Index)
 Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...
 
virtual const GeometryTypeGetGeometryPart (const IndexType Index) const
 Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...
 
virtual GeometryType::Pointer pGetGeometryPart (const IndexType Index)
 Used for composite geometries. It returns the pointer of a geometry part, corresponding to the Index. More...
 
virtual const GeometryType::Pointer pGetGeometryPart (const IndexType Index) const
 Used for composite geometries. It returns the const pointer of a geometry part, corresponding to the Index. More...
 
virtual void SetGeometryPart (const IndexType Index, GeometryType::Pointer pGeometry)
 Allows to exchange certain geometries. More...
 
virtual IndexType AddGeometryPart (GeometryType::Pointer pGeometry)
 Allows to enhance the coupling geometry, with another geometry. More...
 
virtual void RemoveGeometryPart (GeometryType::Pointer pGeometry)
 Removes a geometry part. More...
 
virtual void RemoveGeometryPart (const IndexType Index)
 Removes a geometry part. More...
 
virtual bool HasGeometryPart (const IndexType Index) const
 Use to check if certain Indexed object is within the geometry parts of this geometry. More...
 
virtual SizeType NumberOfGeometryParts () const
 
SizeType WorkingSpaceDimension () const
 
SizeType LocalSpaceDimension () const
 
virtual SizeType PolynomialDegree (IndexType LocalDirectionIndex) const
 Return polynomial degree of the geometry in a certain direction. More...
 
virtual double Volume () const
 This method calculate and return volume of this geometry. More...
 
virtual double MinEdgeLength () const
 
virtual double MaxEdgeLength () const
 
virtual double AverageEdgeLength () const
 
virtual double Circumradius () const
 
virtual double Inradius () const
 
virtual bool HasIntersection (const GeometryType &ThisGeometry) const
 
virtual bool HasIntersection (const Point &rLowPoint, const Point &rHighPoint) const
 
virtual void BoundingBox (TPointType &rLowPoint, TPointType &rHighPoint) const
 Calculates the boundingbox of the geometry. More...
 
virtual Point Center () const
 
virtual array_1d< double, 3 > Normal (const CoordinatesArrayType &rPointLocalCoordinates) const
 It returns a vector that is normal to its corresponding geometry in the given local point. More...
 
virtual array_1d< double, 3 > Normal (IndexType IntegrationPointIndex) const
 It returns the vector, which is normal to its corresponding geometry in the given integration point for the default integration method. More...
 
virtual array_1d< double, 3 > Normal (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 It returns the vector, which is normal to its corresponding geometry in the given integration point. More...
 
virtual array_1d< double, 3 > UnitNormal (const CoordinatesArrayType &rPointLocalCoordinates) const
 It computes the unit normal of the geometry in the given local point. More...
 
virtual array_1d< double, 3 > UnitNormal (IndexType IntegrationPointIndex) const
 It returns the normalized normal vector in the given integration point. More...
 
virtual array_1d< double, 3 > UnitNormal (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 It returns the normalized normal vector in the given integration point. More...
 
double Quality (const QualityCriteria qualityCriteria) const
 
virtual void ComputeDihedralAngles (Vector &rDihedralAngles) const
 
virtual void ComputeSolidAngles (Vector &rSolidAngles) const
 
const PointsArrayTypePoints () const
 
PointsArrayTypePoints ()
 
const TPointType::Pointer pGetPoint (const int Index) const
 
TPointType::Pointer pGetPoint (const int Index)
 
TPointType const & GetPoint (const int Index) const
 
TPointType & GetPoint (const int Index)
 
virtual CoordinatesArrayTypePointLocalCoordinates (CoordinatesArrayType &rResult, const CoordinatesArrayType &rPoint) const
 Returns the local coordinates of a given arbitrary point. More...
 
virtual int IsInsideLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Checks if given point in local space coordinates of this geometry is inside the geometry boundaries. More...
 
virtual void SpansLocalSpace (std::vector< double > &rSpans, IndexType LocalDirectionIndex=0) const
 
virtual GeometriesArrayType GenerateBoundariesEntities () const
 This method gives you all boundaries entities of this geometry. More...
 
virtual GeometriesArrayType GeneratePoints () const
 This method gives you all points of this geometry. More...
 
 KRATOS_DEPRECATED_MESSAGE ("This is legacy version (use GenerateEdges instead)") virtual GeometriesArrayType Edges(void)
 This method gives you all edges of this geometry. More...
 
 KRATOS_DEPRECATED_MESSAGE ("This is legacy version (use GenerateFaces instead)") virtual GeometriesArrayType Faces(void)
 Returns all faces of the current geometry. More...
 
virtual GeometriesArrayType GenerateFaces () const
 Returns all faces of the current geometry. More...
 
SizeType IntegrationPointsNumber () const
 
SizeType IntegrationPointsNumber (IntegrationMethod ThisMethod) const
 
const IntegrationPointsArrayTypeIntegrationPoints () const
 
const IntegrationPointsArrayTypeIntegrationPoints (IntegrationMethod ThisMethod) const
 
virtual void CreateIntegrationPoints (IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo) const
 
virtual void CreateQuadraturePointGeometries (GeometriesArrayType &rResultGeometries, IndexType NumberOfShapeFunctionDerivatives, const IntegrationPointsArrayType &rIntegrationPoints, IntegrationInfo &rIntegrationInfo)
 
virtual void CreateQuadraturePointGeometries (GeometriesArrayType &rResultGeometries, IndexType NumberOfShapeFunctionDerivatives, IntegrationInfo &rIntegrationInfo)
 
virtual CoordinatesArrayTypeGlobalCoordinates (CoordinatesArrayType &rResult, CoordinatesArrayType const &LocalCoordinates) const
 
void GlobalCoordinates (CoordinatesArrayType &rResult, IndexType IntegrationPointIndex) const
 
void GlobalCoordinates (CoordinatesArrayType &rResult, IndexType IntegrationPointIndex, const IntegrationMethod ThisMethod) const
 This method provides the global coordinates to the corresponding integration point. More...
 
virtual CoordinatesArrayTypeGlobalCoordinates (CoordinatesArrayType &rResult, CoordinatesArrayType const &LocalCoordinates, Matrix &DeltaPosition) const
 
virtual void GlobalSpaceDerivatives (std::vector< CoordinatesArrayType > &rGlobalSpaceDerivatives, const CoordinatesArrayType &rLocalCoordinates, const SizeType DerivativeOrder) const
 This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. More...
 
virtual void GlobalSpaceDerivatives (std::vector< CoordinatesArrayType > &rGlobalSpaceDerivatives, IndexType IntegrationPointIndex, const SizeType DerivativeOrder) const
 This method maps from dimension space to working space and computes the number of derivatives at the dimension parameter. More...
 
virtual int ProjectionPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rProjectedPointGlobalCoordinates, CoordinatesArrayType &rProjectedPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. More...
 
virtual int ProjectionPointLocalToLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, CoordinatesArrayType &rProjectionPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Projects a point onto the geometry Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. This function requires an initial guess, provided by rProjectionPointLocalCoordinates. This function can be a very costly operation. More...
 
virtual int ProjectionPointGlobalToLocalSpace (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rProjectionPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Projects a point onto the geometry Projects a certain point on the geometry, or finds the closest point, depending on the provided initial guess. The external point does not necessary lay on the geometry. It shall deal as the interface to the mathematical projection function e.g. the Newton-Raphson. Thus, the breaking criteria does not necessarily mean that it found a point on the surface, if it is really the closest if or not. It shows only if the breaking criteria, defined by the tolerance is reached. This function requires an initial guess, provided by rProjectionPointLocalCoordinates. This function can be a very costly operation. More...
 
virtual int ClosestPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Returns all coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...
 
virtual int ClosestPoint (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Returns global coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...
 
virtual int ClosestPointLocalCoordinates (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Returns local coordinates of the closest point on the geometry given to an arbitrary point in global coordinates. The basic concept is to first do a projection towards this geometry and second checking if the projection was successfull or if no point on the geometry was found. More...
 
virtual int ClosestPointLocalToLocalSpace (const CoordinatesArrayType &rPointLocalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Calculates the closes point projection This method calculates the closest point projection of a point in local space coordinates. More...
 
virtual int ClosestPointGlobalToLocalSpace (const CoordinatesArrayType &rPointGlobalCoordinates, CoordinatesArrayType &rClosestPointLocalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Calculates the closes point projection This method calculates the closest point projection of a point in global space coordinates. More...
 
virtual double CalculateDistance (const CoordinatesArrayType &rPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const
 Computes the distance between an point in global coordinates and the closest point of this geometry. If projection fails, double::max will be returned. More...
 
JacobiansTypeJacobian (JacobiansType &rResult) const
 
virtual JacobiansTypeJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const
 
virtual JacobiansTypeJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod, Matrix &DeltaPosition) const
 
MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const
 
virtual MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual MatrixJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod, const Matrix &rDeltaPosition) const
 
virtual MatrixJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const
 
virtual MatrixJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates, Matrix &rDeltaPosition) const
 
VectorDeterminantOfJacobian (Vector &rResult) const
 
virtual VectorDeterminantOfJacobian (Vector &rResult, IntegrationMethod ThisMethod) const
 
double DeterminantOfJacobian (IndexType IntegrationPointIndex) const
 
virtual double DeterminantOfJacobian (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual double DeterminantOfJacobian (const CoordinatesArrayType &rPoint) const
 
JacobiansTypeInverseOfJacobian (JacobiansType &rResult) const
 
virtual JacobiansTypeInverseOfJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const
 
MatrixInverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const
 
virtual MatrixInverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
virtual MatrixInverseOfJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const
 
const MatrixShapeFunctionsValues () const
 
const MatrixShapeFunctionsValues (IntegrationMethod ThisMethod) const
 
double ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex) const
 
double ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const
 
const ShapeFunctionsGradientsTypeShapeFunctionsLocalGradients () const
 
const ShapeFunctionsGradientsTypeShapeFunctionsLocalGradients (IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const
 
const MatrixShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex) const
 
void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult) const
 
virtual void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, IntegrationMethod ThisMethod) const
 
virtual void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &rDeterminantsOfJacobian, IntegrationMethod ThisMethod) const
 
virtual void ShapeFunctionsIntegrationPointsGradients (ShapeFunctionsGradientsType &rResult, Vector &rDeterminantsOfJacobian, IntegrationMethod ThisMethod, Matrix &ShapeFunctionsIntegrationPointsValues) const
 
virtual int Check () const
 
virtual std::string Name () const
 Returns name. More...
 
virtual void PrintName (std::ostream &rOstream) const
 Print name. More...
 
 KRATOS_CLASS_POINTER_DEFINITION (Geometry)
 Pointer definition of Geometry. More...
 
bool empty () const
 
bool HasIntegrationMethod (IntegrationMethod ThisMethod) const
 
IntegrationMethod GetDefaultIntegrationMethod () const
 
virtual IntegrationInfo GetDefaultIntegrationInfo () const
 Provides the default integration per geometry. More...
 
virtual bool IsSymmetric () const
 
IndexType const & Id () const
 Id of this Geometry. More...
 
bool IsIdGeneratedFromString ()
 Returns if id was generated from a geometry name. More...
 
bool IsIdSelfAssigned ()
 Returns if id was generated by itself. More...
 
void SetId (const IndexType Id)
 Sets Id of this Geometry. More...
 
void SetId (const std::string &rName)
 Sets Id with the use of the name of this geometry. More...
 

Friends

Private Friends
template<class TOtherPointType >
class Triangle2D15
 
- Friends inherited from Kratos::Geometry< TPointType >

Type Definitions

typedef Geometry< TPointType > BaseType
 
typedef Line2D5< TPointType > EdgeType
 
typedef GeometryData::IntegrationMethod IntegrationMethod
 
typedef BaseType::GeometriesArrayType GeometriesArrayType
 
typedef TPointType PointType
 
typedef BaseType::IndexType IndexType
 
typedef BaseType::SizeType SizeType
 
typedef BaseType::PointsArrayType PointsArrayType
 
typedef BaseType::CoordinatesArrayType CoordinatesArrayType
 
typedef BaseType::IntegrationPointType IntegrationPointType
 
typedef BaseType::IntegrationPointsArrayType IntegrationPointsArrayType
 
typedef BaseType::IntegrationPointsContainerType IntegrationPointsContainerType
 
typedef BaseType::ShapeFunctionsValuesContainerType ShapeFunctionsValuesContainerType
 
typedef BaseType::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType
 
typedef BaseType::JacobiansType JacobiansType
 
typedef BaseType::ShapeFunctionsGradientsType ShapeFunctionsGradientsType
 
typedef BaseType::ShapeFunctionsSecondDerivativesType ShapeFunctionsSecondDerivativesType
 
typedef BaseType::ShapeFunctionsThirdDerivativesType ShapeFunctionsThirdDerivativesType
 
typedef BaseType::NormalType NormalType
 
 KRATOS_CLASS_POINTER_DEFINITION (Triangle2D15)
 

Serialization

class Serializer
 

Additional Inherited Members

- Public Types inherited from Kratos::Geometry< TPointType >
enum class  QualityCriteria {
  INRADIUS_TO_CIRCUMRADIUS , AREA_TO_LENGTH , SHORTEST_ALTITUDE_TO_LENGTH , INRADIUS_TO_LONGEST_EDGE ,
  SHORTEST_TO_LONGEST_EDGE , REGULARITY , VOLUME_TO_SURFACE_AREA , VOLUME_TO_EDGE_LENGTH ,
  VOLUME_TO_AVERAGE_EDGE_LENGTH , VOLUME_TO_RMS_EDGE_LENGTH , MIN_DIHEDRAL_ANGLE , MAX_DIHEDRAL_ANGLE ,
  MIN_SOLID_ANGLE
}
 
enum class  LumpingMethods { ROW_SUM , DIAGONAL_SCALING , QUADRATURE_ON_NODES }
 This defines the different methods to compute the lumping methods. More...
 
typedef Geometry< TPointType > GeometryType
 This Geometry type. More...
 
typedef PointerVector< TPointType > PointsArrayType
 
typedef GeometryData::IntegrationMethod IntegrationMethod
 
typedef PointerVector< GeometryTypeGeometriesArrayType
 
typedef TPointType PointType
 
typedef std::size_t IndexType
 
typedef std::size_t SizeType
 
typedef PointType::CoordinatesArrayType CoordinatesArrayType
 
typedef IntegrationPoint< 3 > IntegrationPointType
 
typedef std::vector< IntegrationPointTypeIntegrationPointsArrayType
 
typedef std::array< IntegrationPointsArrayType, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)> IntegrationPointsContainerType
 
typedef std::array< Matrix, static_cast< int >GeometryData::IntegrationMethod::NumberOfIntegrationMethods)> ShapeFunctionsValuesContainerType
 
typedef GeometryData::ShapeFunctionsLocalGradientsContainerType ShapeFunctionsLocalGradientsContainerType
 
typedef DenseVector< MatrixJacobiansType
 
typedef GeometryData::ShapeFunctionsGradientsType ShapeFunctionsGradientsType
 
typedef GeometryData::ShapeFunctionsSecondDerivativesType ShapeFunctionsSecondDerivativesType
 
typedef GeometryData::ShapeFunctionsThirdDerivativesType ShapeFunctionsThirdDerivativesType
 
typedef DenseVector< doubleNormalType
 
typedef PointType::Pointer PointPointerType
 data type stores in this container. More...
 
typedef const PointPointerType ConstPointPointerType
 
typedef TPointType & PointReferenceType
 
typedef const TPointType & ConstPointReferenceType
 
typedef std::vector< PointPointerTypePointPointerContainerType
 
typedef PointsArrayType::iterator iterator
 PointsArrayType typedefs. More...
 
typedef PointsArrayType::const_iterator const_iterator
 
typedef PointsArrayType::ptr_iterator ptr_iterator
 
typedef PointsArrayType::ptr_const_iterator ptr_const_iterator
 
typedef PointsArrayType::difference_type difference_type
 
- Static Public Member Functions inherited from Kratos::Geometry< TPointType >
static bool HasSameType (const GeometryType &rLHS, const GeometryType &rRHS)
 Checks if two GeometryType have the same type. More...
 
static bool HasSameType (const GeometryType *rLHS, const GeometryType *rRHS)
 Checks if two GeometryType have the same type (pointer version) More...
 
static bool HasSameGeometryType (const GeometryType &rLHS, const GeometryType &rRHS)
 Checks if two GeometryType have the same geometry type. More...
 
static bool HasSameGeometryType (const GeometryType *rLHS, const GeometryType *rRHS)
 Checks if two GeometryType have the same geometry type (pointer version) More...
 
static bool IsSame (const GeometryType &rLHS, const GeometryType &rRHS)
 Checks if two GeometryType are the same. More...
 
static bool IsSame (const GeometryType *rLHS, const GeometryType *rRHS)
 Checks if two GeometryType are the same (pointer version) More...
 
static IndexType GenerateId (const std::string &rName)
 Gets the corresponding hash-Id to a string name. More...
 
- Static Public Attributes inherited from Kratos::Geometry< TPointType >
static constexpr IndexType BACKGROUND_GEOMETRY_INDEX = std::numeric_limits<IndexType>::max()
 
- Protected Member Functions inherited from Kratos::Geometry< TPointType >
void SetGeometryData (GeometryData const *pGeometryData)
 updates the pointer to GeometryData of the respective geometry. More...
 
virtual double InradiusToCircumradiusQuality () const
 Quality functions. More...
 
virtual double AreaToEdgeLengthRatio () const
 
virtual double ShortestAltitudeToEdgeLengthRatio () const
 
virtual double InradiusToLongestEdgeQuality () const
 
virtual double ShortestToLongestEdgeQuality () const
 
virtual double RegularityQuality () const
 
virtual double VolumeToSurfaceAreaQuality () const
 
virtual double VolumeToEdgeLengthQuality () const
 
virtual double VolumeToAverageEdgeLength () const
 
virtual double VolumeToRMSEdgeLength () const
 
virtual double MinDihedralAngle () const
 
virtual double MaxDihedralAngle () const
 
virtual double MinSolidAngle () const
 
bool AllPointsAreValid () const
 Checks if the geometry points are valid Checks if the geometry points are valid from the pointer value Points are not valid when the pointer value is null. More...
 

Detailed Description

template<class TPointType>
class Kratos::Triangle2D15< TPointType >

A fifteen node 2D triangular geometry with quartic shape functions.

While the shape functions are only defined in 2D it is possible to define an arbitrary orientation in space. Thus it can be used for defining surfaces on 3D elements. The node ordering corresponds with: 2 |`\ 9 8 | `\ 10 14 7 | `\ 11 12 13 6 | `\ 0–3–4–5–1

Author
Mohamed Nabi

Member Typedef Documentation

◆ BaseType

template<class TPointType >
typedef Geometry<TPointType> Kratos::Triangle2D15< TPointType >::BaseType

Geometry as base class.

◆ CoordinatesArrayType

template<class TPointType >
typedef BaseType::CoordinatesArrayType Kratos::Triangle2D15< TPointType >::CoordinatesArrayType

Array of coordinates. Can be Nodes, Points or IntegrationPoints

◆ EdgeType

template<class TPointType >
typedef Line2D5<TPointType> Kratos::Triangle2D15< TPointType >::EdgeType

Type of edge geometry

◆ GeometriesArrayType

template<class TPointType >
typedef BaseType::GeometriesArrayType Kratos::Triangle2D15< TPointType >::GeometriesArrayType

A Vector of counted pointers to Geometries. Used for returning edges of the geometry.

◆ IndexType

template<class TPointType >
typedef BaseType::IndexType Kratos::Triangle2D15< TPointType >::IndexType

Type used for indexing in geometry class. std::size_t used for indexing point or integration point access methods and also all other methods which need point or integration point index.

◆ IntegrationMethod

template<class TPointType >
typedef GeometryData::IntegrationMethod Kratos::Triangle2D15< TPointType >::IntegrationMethod

Integration methods implemented in geometry.

◆ IntegrationPointsArrayType

template<class TPointType >
typedef BaseType::IntegrationPointsArrayType Kratos::Triangle2D15< TPointType >::IntegrationPointsArrayType

A Vector of IntegrationPointType which used to hold integration points related to an integration method. IntegrationPoints functions used this type to return their results.

◆ IntegrationPointsContainerType

A Vector of IntegrationPointsArrayType which used to hold integration points related to different integration method implemented in geometry.

◆ IntegrationPointType

template<class TPointType >
typedef BaseType::IntegrationPointType Kratos::Triangle2D15< TPointType >::IntegrationPointType

This type used for representing an integration point in geometry. This integration point is a point with an additional weight component.

◆ JacobiansType

template<class TPointType >
typedef BaseType::JacobiansType Kratos::Triangle2D15< TPointType >::JacobiansType

A third order tensor to hold jacobian matrices evaluated at integration points. Jacobian and InverseOfJacobian functions return this type as their result.

◆ NormalType

template<class TPointType >
typedef BaseType::NormalType Kratos::Triangle2D15< TPointType >::NormalType

Type of the normal vector used for normal to edges in geometry.

◆ PointsArrayType

template<class TPointType >
typedef BaseType::PointsArrayType Kratos::Triangle2D15< TPointType >::PointsArrayType

Array of counted pointers to point. This type used to hold geometry's points.

◆ PointType

template<class TPointType >
typedef TPointType Kratos::Triangle2D15< TPointType >::PointType

Redefinition of template parameter TPointType.

◆ ShapeFunctionsGradientsType

A third order tensor to hold shape functions' local gradients. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsLocalGradientsContainerType

A fourth order tensor used as shape functions' local gradients container in geometry.

◆ ShapeFunctionsSecondDerivativesType

A third order tensor to hold shape functions' local second derivatives. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsThirdDerivativesType

A third order tensor to hold shape functions' local third derivatives. ShapefunctionsLocalGradients function return this type as its result.

◆ ShapeFunctionsValuesContainerType

A third order tensor used as shape functions' values container.

◆ SizeType

template<class TPointType >
typedef BaseType::SizeType Kratos::Triangle2D15< TPointType >::SizeType

This type is used to return size or dimension in geometry. Dimension, WorkingDimension, PointsNumber and ... return this type as their results.

Constructor & Destructor Documentation

◆ Triangle2D15() [1/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( const PointType Point01,
const PointType Point02,
const PointType Point03,
const PointType Point04,
const PointType Point05,
const PointType Point06,
const PointType Point07,
const PointType Point08,
const PointType Point09,
const PointType Point10,
const PointType Point11,
const PointType Point12,
const PointType Point13,
const PointType Point14,
const PointType Point15 
)
inline

◆ Triangle2D15() [2/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( typename PointType::Pointer  pPoint01,
typename PointType::Pointer  pPoint02,
typename PointType::Pointer  pPoint03,
typename PointType::Pointer  pPoint04,
typename PointType::Pointer  pPoint05,
typename PointType::Pointer  pPoint06,
typename PointType::Pointer  pPoint07,
typename PointType::Pointer  pPoint08,
typename PointType::Pointer  pPoint09,
typename PointType::Pointer  pPoint10,
typename PointType::Pointer  pPoint11,
typename PointType::Pointer  pPoint12,
typename PointType::Pointer  pPoint13,
typename PointType::Pointer  pPoint14,
typename PointType::Pointer  pPoint15 
)
inline

◆ Triangle2D15() [3/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( const PointsArrayType ThisPoints)
inline

◆ Triangle2D15() [4/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( const IndexType  GeometryId,
const PointsArrayType rThisPoints 
)
inlineexplicit

Constructor with Geometry Id.

◆ Triangle2D15() [5/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( const std::string &  rGeometryName,
const PointsArrayType rThisPoints 
)
inlineexplicit

Constructor with Geometry Name.

◆ Triangle2D15() [6/7]

template<class TPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( Triangle2D15< TPointType > const &  rOther)
inline

Copy constructor. Construct this geometry as a copy of given geometry.

Note
This copy constructor does not copy the points and new geometry shares points with given source geometry. It is obvious that any change to this new geometry's point affect source geometry's points too.

◆ Triangle2D15() [7/7]

template<class TPointType >
template<class TOtherPointType >
Kratos::Triangle2D15< TPointType >::Triangle2D15 ( Triangle2D15< TOtherPointType > const &  rOther)
inline

Copy constructor from a geometry with other point type. Construct this geometry as a copy of given geometry which has different type of points. The given goemetry's TOtherPointType* must be implicity convertible to this geometry PointType.

Note
This copy constructor does not copy the points and new geometry shares points with given source geometry. It is obvious that any change to this new geometry's point affect source geometry's points too.

◆ ~Triangle2D15()

template<class TPointType >
Kratos::Triangle2D15< TPointType >::~Triangle2D15 ( )
inlineoverride

Destructor. Does nothing!!!

Member Function Documentation

◆ Area()

template<class TPointType >
double Kratos::Triangle2D15< TPointType >::Area ( ) const
inlineoverridevirtual

This method calculates and returns area or surface area of this geometry depending to it's dimension. For one dimensional geometry it returns zero, for two dimensional it gives area and for three dimensional geometries it gives surface area.

Returns
double value contains area or surfacede area.
See also
Length()
Volume()
DomainSize()

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [1/4]

template<class TPointType >
BaseType::Pointer Kratos::Triangle2D15< TPointType >::Create ( const BaseType rGeometry) const
inlineoverride

Creates a new geometry pointer.

Parameters
rGeometryreference to an existing geometry
Returns
Pointer to the new geometry

◆ Create() [2/4]

template<class TPointType >
BaseType::Pointer Kratos::Triangle2D15< TPointType >::Create ( const IndexType  NewGeometryId,
const BaseType rGeometry 
) const
inlineoverride

Creates a new geometry pointer.

Parameters
NewGeometryIdthe ID of the new geometry
rGeometryreference to an existing geometry
Returns
Pointer to the new geometry

◆ Create() [3/4]

template<class TPointType >
BaseType::Pointer Kratos::Triangle2D15< TPointType >::Create ( const IndexType  NewGeometryId,
PointsArrayType const &  rThisPoints 
) const
inlineoverridevirtual

Creates a new geometry pointer.

Parameters
NewGeometryIdthe ID of the new geometry
rThisPointsthe nodes of the new geometry
Returns
Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [4/4]

template<class TPointType >
BaseType::Pointer Kratos::Triangle2D15< TPointType >::Create ( PointsArrayType const &  rThisPoints) const
inlineoverridevirtual

Creates a new geometry pointer.

Parameters
rThisPointsthe nodes of the new geometry
Returns
Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ DomainSize()

template<class TPointType >
double Kratos::Triangle2D15< TPointType >::DomainSize ( ) const
inlineoverridevirtual

This method calculates and returns length, area or volume of this geometry depending to it's dimension. For one dimensional geometry it returns its length, for two dimensional it gives area and for three dimensional geometries it gives its volume.

Returns
double value contains length, area or volume.
See also
Length()
Area()
Volume()

Reimplemented from Kratos::Geometry< TPointType >.

◆ EdgesNumber()

template<class TPointType >
SizeType Kratos::Triangle2D15< TPointType >::EdgesNumber ( ) const
inlineoverridevirtual

This method gives you number of all edges of this geometry.

For example, for a hexahedron, this would be 12

Returns
SizeType containes number of this geometry edges.
See also
EdgesNumber()
Edges()
GenerateEdges()
FacesNumber()
Faces()
GenerateFaces()

Reimplemented from Kratos::Geometry< TPointType >.

◆ FacesNumber()

template<class TPointType >
SizeType Kratos::Triangle2D15< TPointType >::FacesNumber ( ) const
inlineoverridevirtual

Returns the number of faces of the current geometry.

This is only implemented for 3D geometries, since 2D geometries only have edges but no faces

See also
EdgesNumber
Edges
Faces

Reimplemented from Kratos::Geometry< TPointType >.

◆ GenerateEdges()

template<class TPointType >
GeometriesArrayType Kratos::Triangle2D15< TPointType >::GenerateEdges ( ) const
inlineoverridevirtual

This method gives you all edges of this geometry.

This method will gives you all the edges with one dimension less than this geometry. For example a triangle would return three lines as its edges or a tetrahedral would return four triangle as its edges but won't return its six edge lines by this method.

Returns
GeometriesArrayType containes this geometry edges.
See also
EdgesNumber()
Edge()

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryFamily()

template<class TPointType >
GeometryData::KratosGeometryFamily Kratos::Triangle2D15< TPointType >::GetGeometryFamily ( ) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryType()

template<class TPointType >
GeometryData::KratosGeometryType Kratos::Triangle2D15< TPointType >::GetGeometryType ( ) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ Info()

template<class TPointType >
std::string Kratos::Triangle2D15< TPointType >::Info ( ) const
inlineoverridevirtual

Turn back information as a string.

Returns
String contains information about this geometry.
See also
PrintData()
PrintInfo()

Reimplemented from Kratos::Geometry< TPointType >.

◆ IsInside()

template<class TPointType >
bool Kratos::Triangle2D15< TPointType >::IsInside ( const CoordinatesArrayType rPoint,
CoordinatesArrayType rResult,
const double  Tolerance = std::numeric_limits<double>::epsilon() 
) const
inlineoverridevirtual

Returns whether given arbitrary point is inside the Geometry and the respective local point for the given global point.

Parameters
rPointThe point to be checked if is inside o note in global coordinates
rResultThe local coordinates of the point
ToleranceThe tolerance that will be considered to check if the point is inside or not
Returns
True if the point is inside, false otherwise

Reimplemented from Kratos::Geometry< TPointType >.

◆ KRATOS_CLASS_POINTER_DEFINITION()

template<class TPointType >
Kratos::Triangle2D15< TPointType >::KRATOS_CLASS_POINTER_DEFINITION ( Triangle2D15< TPointType >  )

Pointer definition of Triangle2D15

◆ Length()

template<class TPointType >
double Kratos::Triangle2D15< TPointType >::Length ( ) const
inlineoverridevirtual

This method calculates and returns Length or charactereistic length of this geometry depending on it's dimension. For one dimensional geometry for example Line it returns length of it and for the other geometries it gives Characteristic length otherwise. In the current geometry this function returns the determinant of jacobian

Returns
double value contains length or Characteristic length
See also
Area()
Volume()
DomainSize()

Reimplemented from Kratos::Geometry< TPointType >.

◆ NodesInFaces()

template<class TPointType >
void Kratos::Triangle2D15< TPointType >::NodesInFaces ( DenseMatrix< unsigned int > &  NodesInFaces) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ NumberNodesInFaces()

template<class TPointType >
void Kratos::Triangle2D15< TPointType >::NumberNodesInFaces ( DenseVector< unsigned int > &  NumberNodesInFaces) const
inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ operator=() [1/2]

template<class TPointType >
Triangle2D15& Kratos::Triangle2D15< TPointType >::operator= ( const Triangle2D15< TPointType > &  rOther)
inline

Assignment operator.

Note
This operator don't copy the points and this geometry shares points with given source geometry. It's obvious that any change to this geometry's point affect source geometry's points too.
See also
Clone
ClonePoints

◆ operator=() [2/2]

template<class TPointType >
template<class TOtherPointType >
Triangle2D15& Kratos::Triangle2D15< TPointType >::operator= ( Triangle2D15< TOtherPointType > const &  rOther)
inline

Assignment operator for geometries with different point type.

Note
This operator don't copy the points and this geometry shares points with given source geometry. It's obvious that any change to this geometry's point affect source geometry's points too.
See also
Clone
ClonePoints

◆ PointsLocalCoordinates()

template<class TPointType >
Matrix& Kratos::Triangle2D15< TPointType >::PointsLocalCoordinates ( Matrix rResult) const
inlineoverridevirtual

returns the local coordinates of all nodes of the current geometry

Parameters
rResulta Matrix object that will be overwritten by the result
Returns
the local coordinates of all nodes

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintData()

template<class TPointType >
void Kratos::Triangle2D15< TPointType >::PrintData ( std::ostream &  rOStream) const
inlineoverridevirtual

Print geometry's data into given stream. Prints it's points by the order they stored in the geometry and then center point of geometry.

Parameters
rOStreamStream to print into it.
See also
PrintInfo()
Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintInfo()

template<class TPointType >
void Kratos::Triangle2D15< TPointType >::PrintInfo ( std::ostream &  rOStream) const
inlineoverridevirtual

Print information about this object.

Parameters
rOStreamStream to print into it.
See also
PrintData()
Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsGradients()

template<class TPointType >
virtual Matrix& Kratos::Triangle2D15< TPointType >::ShapeFunctionsGradients ( Matrix rResult,
const CoordinatesArrayType rPoint 
)
inlinevirtual

returns the shape function gradients in an arbitrary point, given in local coordinates

Parameters
rResultthe matrix of gradients, will be overwritten with the gradients for all shape functions in given point
rPointthe given point the gradients are calculated in

◆ ShapeFunctionsLocalGradients() [1/3]

template<class TPointType >
virtual ShapeFunctionsGradientsType Kratos::Triangle2D15< TPointType >::ShapeFunctionsLocalGradients ( )
inlinevirtual

Calculates the local gradients for all integration points for the default integration method

◆ ShapeFunctionsLocalGradients() [2/3]

template<class TPointType >
virtual ShapeFunctionsGradientsType Kratos::Triangle2D15< TPointType >::ShapeFunctionsLocalGradients ( IntegrationMethod  ThisMethod)
inlinevirtual

Calculates the local gradients for all integration points for given integration method

◆ ShapeFunctionsLocalGradients() [3/3]

template<class TPointType >
Matrix& Kratos::Triangle2D15< TPointType >::ShapeFunctionsLocalGradients ( Matrix rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

Calculates the gradients in terms of local coordinates of all shape functions in a given point.

Parameters
rPointthe current point at which the gradients are calculated in local coordinates
Returns
the gradients of all shape functions \( \frac{\partial N^i}{\partial \xi_j} \)

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsSecondDerivatives()

template<class TPointType >
ShapeFunctionsSecondDerivativesType& Kratos::Triangle2D15< TPointType >::ShapeFunctionsSecondDerivatives ( ShapeFunctionsSecondDerivativesType rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

returns the second order derivatives of all shape functions in given arbitrary pointers

Parameters
rResulta third order tensor which contains the second derivatives
rPointthe given point the second order derivatives are calculated in

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsThirdDerivatives()

template<class TPointType >
ShapeFunctionsThirdDerivativesType& Kratos::Triangle2D15< TPointType >::ShapeFunctionsThirdDerivatives ( ShapeFunctionsThirdDerivativesType rResult,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

returns the third order derivatives of all shape functions in given arbitrary pointers

Parameters
rResulta fourth order tensor which contains the third derivatives
rPointthe given point the third order derivatives are calculated in

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsValues()

template<class TPointType >
Vector& Kratos::Triangle2D15< TPointType >::ShapeFunctionsValues ( Vector rResult,
const CoordinatesArrayType rCoordinates 
) const
inlineoverridevirtual

Returns vector of shape function values at local coordinate.

For a definition of the shape functions see, e.g., https://www.colorado.edu/engineering/CAS/courses.d/IFEM.d/IFEM.Ch18.d/IFEM.Ch18.pdf.

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionValue()

template<class TPointType >
double Kratos::Triangle2D15< TPointType >::ShapeFunctionValue ( IndexType  ShapeFunctionIndex,
const CoordinatesArrayType rPoint 
) const
inlineoverridevirtual

Calculates the value of a given shape function at a given point.

Parameters
ShapeFunctionIndexThe number of the desired shape function
rPointthe given point in local coordinates at which the value of the shape function is calculated
Returns
the value of the shape function at the given point

Reimplemented from Kratos::Geometry< TPointType >.

Friends And Related Function Documentation

◆ Serializer

template<class TPointType >
friend class Serializer
friend

◆ Triangle2D15

template<class TPointType >
template<class TOtherPointType >
friend class Triangle2D15
friend

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