An eight node hexahedra geometry with linear shape functions. More...

#include <hexahedra_3d_8.h>

Inheritance diagram for Kratos::Hexahedra3D8< TPointType >:

Collaboration diagram for Kratos::Hexahedra3D8< TPointType >:

Public Types
typedef Geometry< TPointType >	BaseType

typedef Line3D2< TPointType >	EdgeType

typedef Quadrilateral3D4< TPointType >	FaceType

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::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::NormalType	NormalType

typedef BaseType::CoordinatesArrayType	CoordinatesArrayType

typedef Matrix	MatrixType

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< GeometryType >	GeometriesArrayType

typedef TPointType	PointType

typedef std::size_t	IndexType

typedef std::size_t	SizeType

typedef PointType::CoordinatesArrayType	CoordinatesArrayType

typedef IntegrationPoint< 3 >	IntegrationPointType

typedef std::vector< IntegrationPointType >	IntegrationPointsArrayType

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< Matrix >	JacobiansType

typedef GeometryData::ShapeFunctionsGradientsType	ShapeFunctionsGradientsType

typedef GeometryData::ShapeFunctionsSecondDerivativesType	ShapeFunctionsSecondDerivativesType

typedef GeometryData::ShapeFunctionsThirdDerivativesType	ShapeFunctionsThirdDerivativesType

typedef DenseVector< double >	NormalType

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< PointPointerType >	PointPointerContainerType

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

Public Member Functions
	KRATOS_CLASS_POINTER_DEFINITION (Hexahedra3D8)

	Hexahedra3D8 (const PointType &Point1, const PointType &Point2, const PointType &Point3, const PointType &Point4, const PointType &Point5, const PointType &Point6, const PointType &Point7, const PointType &Point8)

	Hexahedra3D8 (typename PointType::Pointer pPoint1, typename PointType::Pointer pPoint2, typename PointType::Pointer pPoint3, typename PointType::Pointer pPoint4, typename PointType::Pointer pPoint5, typename PointType::Pointer pPoint6, typename PointType::Pointer pPoint7, typename PointType::Pointer pPoint8)

	Hexahedra3D8 (const PointsArrayType &ThisPoints)

	Hexahedra3D8 (const IndexType GeometryId, const PointsArrayType &rThisPoints)
	Constructor with Geometry Id. More...

	Hexahedra3D8 (const std::string &rGeometryName, const PointsArrayType &rThisPoints)
	Constructor with Geometry Name. More...

	Hexahedra3D8 (Hexahedra3D8 const &rOther)

template<class TOtherPointType >
	Hexahedra3D8 (Hexahedra3D8< TOtherPointType > const &rOther)

	~Hexahedra3D8 () override
	Destructor. Does nothing!!! More...

GeometryData::KratosGeometryFamily	GetGeometryFamily () const override

GeometryData::KratosGeometryType	GetGeometryType () const override

Hexahedra3D8 &	operator= (const Hexahedra3D8 &rOther)

template<class TOtherPointType >
Hexahedra3D8 &	operator= (Hexahedra3D8< TOtherPointType > const &rOther)

BaseType::Pointer	Create (const IndexType NewGeometryId, PointsArrayType const &rThisPoints) 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...

double	Length () const override

double	Area () const override

double	Volume () const override
	This method calculate and return volume of this geometry. More...

double	DomainSize () const override

Matrix &	PointsLocalCoordinates (Matrix &rResult) 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...

SizeType	EdgesNumber () const override

GeometriesArrayType	GenerateEdges () const override

double	AverageEdgeLength () const override

double	MaxEdgeLength () const override

double	MinEdgeLength () const override

Face
SizeType	FacesNumber () const override
	Returns the number of faces of the current geometry. More...

GeometriesArrayType	GenerateFaces () const override
	Returns all faces of the current geometry. More...

bool	HasIntersection (const Point &rLowPoint, const Point &rHighPoint) const override

void	ComputeSolidAngles (Vector &rSolidAngles) const override
	Implements the calculus of the 8 solid angles of the hexa. More...

void	ComputeDihedralAngles (Vector &rDihedralAngles) const override
	Implements the calculus of the 24 dihedral angles of the hexa. More...

double	MinDihedralAngle () const override
	Calculates the min dihedral angle quality metric. More...

double	MaxDihedralAngle () const override
	Calculates the max dihedral angle quality metric. More...

double	VolumeToRMSEdgeLength () const override
	Calculates the volume to average edge length quality metric. More...

double	ShortestToLongestEdgeQuality () const override
	Calculates the shortest to longest edge quality metric. Calculates the shortest to longest edge quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value. More...

double	ShapeFunctionValue (IndexType ShapeFunctionIndex, const CoordinatesArrayType &rPoint) const override

Vector &	ShapeFunctionsValues (Vector &rResult, const CoordinatesArrayType &rCoordinates) const override

Matrix &	ShapeFunctionsLocalGradients (Matrix &rResult, const CoordinatesArrayType &rPoint) const override

ShapeFunctionsSecondDerivativesType &	ShapeFunctionsSecondDerivatives (ShapeFunctionsSecondDerivativesType &rResult, const CoordinatesArrayType &rPoint) const override

Spatial Operations
double	CalculateDistance (const CoordinatesArrayType &rPointGlobalCoordinates, const double Tolerance=std::numeric_limits< double >::epsilon()) const override
	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...

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...

Geometry &	operator= (const Geometry &rOther)

template<class TOtherPointType >
Geometry &	operator= (Geometry< TOtherPointType > const &rOther)

	operator PointsArrayType & ()

TPointType &	operator[] (const SizeType &i)

TPointType const &	operator[] (const SizeType &i) const

PointPointerType &	operator() (const SizeType &i)

ConstPointPointerType &	operator() (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 ()

PointPointerContainerType &	GetContainer ()
	‍** Gives a reference to underly normal container. *‍/ More...

const PointPointerContainerType &	GetContainer () const

DataValueContainer &	GetData ()

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...

virtual Pointer	Create (PointsArrayType const &rThisPoints) const
	Creates a new geometry pointer. 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 Vector &	LumpingFactors (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 GeometryType &	GetGeometryParent (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 GeometryType &	GetGeometryPart (const IndexType Index)
	Used for composite geometries. It returns the the geometry part, corresponding to the Index. More...

virtual const GeometryType &	GetGeometryPart (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	Circumradius () const

virtual double	Inradius () const

virtual bool	HasIntersection (const GeometryType &ThisGeometry) 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

const PointsArrayType &	Points () const

PointsArrayType &	Points ()

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 CoordinatesArrayType &	PointLocalCoordinates (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 void	NumberNodesInFaces (DenseVector< unsigned int > &rNumberNodesInFaces) const

virtual void	NodesInFaces (DenseMatrix< unsigned int > &rNodesInFaces) const

SizeType	IntegrationPointsNumber () const

SizeType	IntegrationPointsNumber (IntegrationMethod ThisMethod) const

const IntegrationPointsArrayType &	IntegrationPoints () const

const IntegrationPointsArrayType &	IntegrationPoints (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 CoordinatesArrayType &	GlobalCoordinates (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 CoordinatesArrayType &	GlobalCoordinates (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...

JacobiansType &	Jacobian (JacobiansType &rResult) const

virtual JacobiansType &	Jacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const

virtual JacobiansType &	Jacobian (JacobiansType &rResult, IntegrationMethod ThisMethod, Matrix &DeltaPosition) const

Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex) const

virtual Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

virtual Matrix &	Jacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod, const Matrix &rDeltaPosition) const

virtual Matrix &	Jacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const

virtual Matrix &	Jacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates, Matrix &rDeltaPosition) const

Vector &	DeterminantOfJacobian (Vector &rResult) const

virtual Vector &	DeterminantOfJacobian (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

JacobiansType &	InverseOfJacobian (JacobiansType &rResult) const

virtual JacobiansType &	InverseOfJacobian (JacobiansType &rResult, IntegrationMethod ThisMethod) const

Matrix &	InverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex) const

virtual Matrix &	InverseOfJacobian (Matrix &rResult, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

virtual Matrix &	InverseOfJacobian (Matrix &rResult, const CoordinatesArrayType &rCoordinates) const

const Matrix &	ShapeFunctionsValues () const

const Matrix &	ShapeFunctionsValues (IntegrationMethod ThisMethod) const

double	ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex) const

double	ShapeFunctionValue (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const

const ShapeFunctionsGradientsType &	ShapeFunctionsLocalGradients () const

const ShapeFunctionsGradientsType &	ShapeFunctionsLocalGradients (IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionLocalGradient (IndexType IntegrationPointIndex, IndexType ShapeFunctionIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex, IntegrationMethod ThisMethod) const

const Matrix &	ShapeFunctionDerivatives (IndexType DerivativeOrderIndex, IndexType IntegrationPointIndex) const

virtual ShapeFunctionsThirdDerivativesType &	ShapeFunctionsThirdDerivatives (ShapeFunctionsThirdDerivativesType &rResult, const CoordinatesArrayType &rPoint) 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...

Input and output
std::string	Info () const override

void	PrintInfo (std::ostream &rOStream) const override

void	PrintData (std::ostream &rOStream) const override

Serialization
class	Serializer

template<class TOtherPointType >
class	Hexahedra3D8

Additional Inherited Members
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	RegularityQuality () const

virtual double	VolumeToSurfaceAreaQuality () const

virtual double	VolumeToEdgeLengthQuality () const

virtual double	VolumeToAverageEdgeLength () 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::Hexahedra3D8< TPointType >

An eight node hexahedra geometry with linear shape functions.

The node ordering corresponds with: v 3-------—2 |\ ^ |\ | \ | | \ | \ | | \ | 7---—+—6 | | +– |– | -> u 0—+—--1 | \ | \ \ | \ | \ \ | | w | 4-------—5

Author: Riccardo Rossi; Janosch Stascheit; Felix Nagel

Member Typedef Documentation

◆ BaseType

template<class TPointType >

typedef Geometry<TPointType> Kratos::Hexahedra3D8< TPointType >::BaseType

Type Definitions Geometry as base class.

◆ CoordinatesArrayType

template<class TPointType >

typedef BaseType::CoordinatesArrayType Kratos::Hexahedra3D8< TPointType >::CoordinatesArrayType

Type of coordinates array

◆ EdgeType

template<class TPointType >

typedef Line3D2<TPointType> Kratos::Hexahedra3D8< TPointType >::EdgeType

Type of edge and face geometries

◆ FaceType

template<class TPointType >

typedef Quadrilateral3D4<TPointType> Kratos::Hexahedra3D8< TPointType >::FaceType

◆ GeometriesArrayType

template<class TPointType >

typedef BaseType::GeometriesArrayType Kratos::Hexahedra3D8< TPointType >::GeometriesArrayType

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

◆ IndexType

template<class TPointType >

typedef BaseType::IndexType Kratos::Hexahedra3D8< 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::Hexahedra3D8< TPointType >::IntegrationMethod

Integration methods implemented in geometry.

◆ IntegrationPointsArrayType

template<class TPointType >

typedef BaseType::IntegrationPointsArrayType Kratos::Hexahedra3D8< 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

template<class TPointType >

typedef BaseType::IntegrationPointsContainerType Kratos::Hexahedra3D8< TPointType >::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::Hexahedra3D8< 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::Hexahedra3D8< TPointType >::JacobiansType

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

◆ MatrixType

template<class TPointType >

typedef Matrix Kratos::Hexahedra3D8< TPointType >::MatrixType

Type of Matrix

◆ NormalType

template<class TPointType >

typedef BaseType::NormalType Kratos::Hexahedra3D8< TPointType >::NormalType

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

◆ PointsArrayType

template<class TPointType >

typedef BaseType::PointsArrayType Kratos::Hexahedra3D8< TPointType >::PointsArrayType

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

◆ PointType

template<class TPointType >

typedef TPointType Kratos::Hexahedra3D8< TPointType >::PointType

Redefinition of template parameter TPointType.

◆ ShapeFunctionsGradientsType

template<class TPointType >

typedef BaseType::ShapeFunctionsGradientsType Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsGradientsType

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

◆ ShapeFunctionsLocalGradientsContainerType

template<class TPointType >

typedef BaseType::ShapeFunctionsLocalGradientsContainerType Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsLocalGradientsContainerType

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

◆ ShapeFunctionsSecondDerivativesType

template<class TPointType >

typedef BaseType::ShapeFunctionsSecondDerivativesType Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsSecondDerivativesType

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

◆ ShapeFunctionsValuesContainerType

template<class TPointType >

typedef BaseType::ShapeFunctionsValuesContainerType Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsValuesContainerType

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

◆ SizeType

template<class TPointType >

typedef BaseType::SizeType Kratos::Hexahedra3D8< TPointType >::SizeType

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

Constructor & Destructor Documentation

◆ Hexahedra3D8() [1/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8	(	const PointType &	Point1,
		const PointType &	Point2,
		const PointType &	Point3,
		const PointType &	Point4,
		const PointType &	Point5,
		const PointType &	Point6,
		const PointType &	Point7,
		const PointType &	Point8
	)

inline

Life Cycle

◆ Hexahedra3D8() [2/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8	(	typename PointType::Pointer	pPoint1,
		typename PointType::Pointer	pPoint2,
		typename PointType::Pointer	pPoint3,
		typename PointType::Pointer	pPoint4,
		typename PointType::Pointer	pPoint5,
		typename PointType::Pointer	pPoint6,
		typename PointType::Pointer	pPoint7,
		typename PointType::Pointer	pPoint8
	)

inline

◆ Hexahedra3D8() [3/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8 ( const PointsArrayType & ThisPoints )

inlineexplicit

◆ Hexahedra3D8() [4/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8	(	const IndexType	GeometryId,
		const PointsArrayType &	rThisPoints
	)

inlineexplicit

Constructor with Geometry Id.

◆ Hexahedra3D8() [5/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8	(	const std::string &	rGeometryName,
		const PointsArrayType &	rThisPoints
	)

inlineexplicit

Constructor with Geometry Name.

◆ Hexahedra3D8() [6/7]

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8 ( Hexahedra3D8< TPointType > const & rOther )

inline

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

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

◆ Hexahedra3D8() [7/7]

template<class TPointType >

template<class TOtherPointType >

Kratos::Hexahedra3D8< TPointType >::Hexahedra3D8 ( Hexahedra3D8< TOtherPointType > const & rOther )

inlineexplicit

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 don't copy the points and new geometry shares points with given source geometry. It's obvious that any change to this new geometry's point affect source geometry's points too.

◆ ~Hexahedra3D8()

template<class TPointType >

Kratos::Hexahedra3D8< TPointType >::~Hexahedra3D8 ( )

inlineoverride

Destructor. Does nothing!!!

Member Function Documentation

◆ Area()

template<class TPointType >

double Kratos::Hexahedra3D8< 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 surface area.

See also: Length(); Volume(); DomainSize()

:TODO: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ AverageEdgeLength()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::AverageEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the average edge length of the geometry

Returns: double value with the average edge length

Reimplemented from Kratos::Geometry< TPointType >.

◆ CalculateDistance()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::CalculateDistance	(	const CoordinatesArrayType &	rPointGlobalCoordinates,
		const double	Tolerance = `std::numeric_limits<double>::epsilon()`
	)		const

inlineoverridevirtual

Computes the distance between an point in global coordinates and the closest point of this geometry. If projection fails, double::max will be returned.

Parameters

rPointGlobalCoordinates	the point to which the closest point has to be found.
Tolerance	accepted orthogonal error.

Returns: Distance to geometry. positive -> outside of to the geometry (for 2D and solids) 0 -> on/ in the geometry.

Reimplemented from Kratos::Geometry< TPointType >.

◆ ComputeDihedralAngles()

template<class TPointType >

void Kratos::Hexahedra3D8< TPointType >::ComputeDihedralAngles ( Vector & rDihedralAngles ) const

inlineoverridevirtual

Implements the calculus of the 24 dihedral angles of the hexa.

Implements the calculus of the 24 dihedral angles of the hexa. Each edge has two different dihedral angles in each extreme.

Parameters

rDihedralAngles The dihedral angles

Reimplemented from Kratos::Geometry< TPointType >.

◆ ComputeSolidAngles()

template<class TPointType >

void Kratos::Hexahedra3D8< TPointType >::ComputeSolidAngles ( Vector & rSolidAngles ) const

inlineoverridevirtual

Implements the calculus of the 8 solid angles of the hexa.

Implements the calculus of the 8 solid angles of the hexa

Parameters

rSolidAngles The solid angles of the geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ Create() [1/2]

template<class TPointType >

BaseType::Pointer Kratos::Hexahedra3D8< TPointType >::Create	(	const IndexType	NewGeometryId,
		const BaseType &	rGeometry
	)		const

inlineoverride

Creates a new geometry pointer.

Parameters

NewGeometryId	the ID of the new geometry
rGeometry	reference to an existing geometry

Returns: Pointer to the new geometry

◆ Create() [2/2]

template<class TPointType >

BaseType::Pointer Kratos::Hexahedra3D8< TPointType >::Create	(	const IndexType	NewGeometryId,
		PointsArrayType const &	rThisPoints
	)		const

inlineoverridevirtual

Creates a new geometry pointer.

Operations

Parameters

NewGeometryId	the ID of the new geometry
rThisPoints	the nodes of the new geometry

Returns: Pointer to the new geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ DomainSize()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::DomainSize ( ) const

inlineoverridevirtual

This method calculate and return 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()

:TODO: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ EdgesNumber()

template<class TPointType >

SizeType Kratos::Hexahedra3D8< TPointType >::EdgesNumber ( ) const

inlineoverridevirtual

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

Returns: SizeType containes number of this geometry edges.

See also: Edges(); Edge()

Reimplemented from Kratos::Geometry< TPointType >.

◆ FacesNumber()

template<class TPointType >

SizeType Kratos::Hexahedra3D8< 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::Hexahedra3D8< TPointType >::GenerateEdges ( ) const

inlineoverridevirtual

This method gives you all edges of this geometry.

Returns: GeometriesArrayType containes this geometry edges.

See also: EdgesNumber(); Edge()

Reimplemented from Kratos::Geometry< TPointType >.

◆ GenerateFaces()

template<class TPointType >

GeometriesArrayType Kratos::Hexahedra3D8< TPointType >::GenerateFaces ( ) const

inlineoverridevirtual

Returns all faces of the current geometry.

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

Returns: GeometriesArrayType containes this geometry faces.

See also: EdgesNumber; GenerateEdges; FacesNumber

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryFamily()

template<class TPointType >

GeometryData::KratosGeometryFamily Kratos::Hexahedra3D8< TPointType >::GetGeometryFamily ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ GetGeometryType()

template<class TPointType >

GeometryData::KratosGeometryType Kratos::Hexahedra3D8< TPointType >::GetGeometryType ( ) const

inlineoverridevirtual

Reimplemented from Kratos::Geometry< TPointType >.

◆ HasIntersection()

template<class TPointType >

bool Kratos::Hexahedra3D8< TPointType >::HasIntersection	(	const Point &	rLowPoint,
		const Point &	rHighPoint
	)		const

inlineoverridevirtual

Test intersection of the geometry with a box

Tests the intersection of the geometry with a 3D box defined by rLowPoint and rHighPoint

Parameters

rLowPoint	Lower point of the box to test the intersection
rHighPoint	Higher point of the box to test the intersection

Returns: True if the geometry intersects the box, False in any other case.

Reimplemented from Kratos::Geometry< TPointType >.

◆ Info()

template<class TPointType >

std::string Kratos::Hexahedra3D8< 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::Hexahedra3D8< 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

rPoint	The point to be checked if is inside o note in global coordinates
rResult	The local coordinates of the point
Tolerance	The 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::Hexahedra3D8< TPointType >::KRATOS_CLASS_POINTER_DEFINITION ( Hexahedra3D8< TPointType > )

Pointer definition of Hexahedra3D8

◆ Length()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::Length ( ) const

inlineoverridevirtual

Information 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.

Returns: double value contains length or Characteristic length

See also: Area(); Volume(); DomainSize()

:TODO: might be necessary to reimplement

Reimplemented from Kratos::Geometry< TPointType >.

◆ MaxDihedralAngle()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::MaxDihedralAngle ( ) const

inlineoverridevirtual

Calculates the max dihedral angle quality metric.

Calculates the max dihedral angle quality metric. The max dihedral angle is max angle between two faces of the element in radians

Returns: [description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ MaxEdgeLength()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::MaxEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the maximum edge length of the geometry

Returns: double value with the maximum edge length

See also: MinEdgeLength(); AverageEdgeLength()

Reimplemented from Kratos::Geometry< TPointType >.

◆ MinDihedralAngle()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::MinDihedralAngle ( ) const

inlineoverridevirtual

Calculates the min dihedral angle quality metric.

Calculates the min dihedral angle quality metric. The min dihedral angle is min angle between two faces of the element in radians

Returns: [description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ MinEdgeLength()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::MinEdgeLength ( ) const

inlineoverridevirtual

This method calculates and returns the minimum edge length of the geometry

Returns: double value with the maximum edge length

See also: MaxEdgeLength(); AverageEdgeLength()

Reimplemented from Kratos::Geometry< TPointType >.

◆ operator=() [1/2]

template<class TPointType >

Hexahedra3D8& Kratos::Hexahedra3D8< TPointType >::operator= ( const Hexahedra3D8< TPointType > & rOther )

inline

Operators 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 >

Hexahedra3D8& Kratos::Hexahedra3D8< TPointType >::operator= ( Hexahedra3D8< 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::Hexahedra3D8< TPointType >::PointsLocalCoordinates ( Matrix & rResult ) const

inlineoverridevirtual

Returns a matrix of the local coordinates of all points

Parameters

rResult a Matrix that will be overwritten by the results

Returns: the coordinates of all points of the current geometry

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintData()

template<class TPointType >

void Kratos::Hexahedra3D8< 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

rOStream Stream to print into it.

See also: PrintInfo(); Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ PrintInfo()

template<class TPointType >

void Kratos::Hexahedra3D8< TPointType >::PrintInfo ( std::ostream & rOStream ) const

inlineoverridevirtual

Print information about this object.

Parameters

rOStream Stream to print into it.

See also: PrintData(); Info()

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsLocalGradients()

template<class TPointType >

Matrix& Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsLocalGradients	(	Matrix &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

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

Parameters

rPoint the current point at which the gradients are calculated

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::Hexahedra3D8< TPointType >::ShapeFunctionsSecondDerivatives	(	ShapeFunctionsSecondDerivativesType &	rResult,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

Calculates the second derivatives in terms of local coordinateds of all shape functions in a given point.

Parameters

rResult	the given container will be overwritten by the results
rPoint	the given local coordinates the derivatives will be evaluated for.

Returns: a third order tensor containing the second order derivatives for each shape function

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionsValues()

template<class TPointType >

Vector& Kratos::Hexahedra3D8< TPointType >::ShapeFunctionsValues	(	Vector &	rResult,
		const CoordinatesArrayType &	rCoordinates
	)		const

inlineoverridevirtual

This method gives all non-zero shape functions values evaluated at the rCoordinates provided

Returns: Vector of values of shape functions \( F_{i} \) where i is the shape function index (for NURBS it is the index of the local enumeration in the element).

See also: ShapeFunctionValue; ShapeFunctionsLocalGradients; ShapeFunctionLocalGradient

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShapeFunctionValue()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::ShapeFunctionValue	(	IndexType	ShapeFunctionIndex,
		const CoordinatesArrayType &	rPoint
	)		const

inlineoverridevirtual

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

Parameters

ShapeFunctionIndex	The number of the desired shape function
rPoint	the 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 TODO: TO BE VERIFIED

Reimplemented from Kratos::Geometry< TPointType >.

◆ ShortestToLongestEdgeQuality()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::ShortestToLongestEdgeQuality ( ) const

inlineoverridevirtual

Calculates the shortest to longest edge quality metric. Calculates the shortest to longest edge quality metric. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value.

\( \frac{l}{L} \)

Returns: [description]

Reimplemented from Kratos::Geometry< TPointType >.

◆ Volume()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::Volume ( ) const

inlineoverridevirtual

This method calculate and return volume of this geometry.

For one and two dimensional geometry it returns zero and for three dimensional it gives volume of geometry.

Returns: double value contains volume.

See also: Length(); Area(); DomainSize()

Reimplemented from Kratos::Geometry< TPointType >.

◆ VolumeToRMSEdgeLength()

template<class TPointType >

double Kratos::Hexahedra3D8< TPointType >::VolumeToRMSEdgeLength ( ) const

inlineoverridevirtual

Calculates the volume to average edge length quality metric.

The average edge length is calculated using the RMS. This metric is bounded by the interval (0,1) being: 1 -> Optimal value 0 -> Worst value

\( \frac{V}{\sqrt{\frac{1}{6}\sum{A_{i}^{2}}}} \)

Returns: [description]

Reimplemented from Kratos::Geometry< TPointType >.

Friends And Related Function Documentation

◆ Hexahedra3D8

template<class TPointType >

template<class TOtherPointType >

friend class Hexahedra3D8

friend

Private Friends

◆ Serializer

template<class TPointType >

friend class Serializer

friend

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

/home/runner/work/Documentation/Documentation/master/kratos/geometries/hexahedra_3d_8.h

Public Types

Public Member Functions

Input and output

Serialization

Additional Inherited Members

Detailed Description

template<class TPointType> class Kratos::Hexahedra3D8< TPointType >

Member Typedef Documentation

◆ BaseType

◆ CoordinatesArrayType

◆ EdgeType

◆ FaceType

◆ GeometriesArrayType

◆ IndexType

◆ IntegrationMethod

◆ IntegrationPointsArrayType

◆ IntegrationPointsContainerType

◆ IntegrationPointType

◆ JacobiansType

◆ MatrixType

◆ NormalType

◆ PointsArrayType

◆ PointType

◆ ShapeFunctionsGradientsType

◆ ShapeFunctionsLocalGradientsContainerType

◆ ShapeFunctionsSecondDerivativesType

◆ ShapeFunctionsValuesContainerType

◆ SizeType

Constructor & Destructor Documentation

◆ Hexahedra3D8() [1/7]

◆ Hexahedra3D8() [2/7]

◆ Hexahedra3D8() [3/7]

◆ Hexahedra3D8() [4/7]

◆ Hexahedra3D8() [5/7]

◆ Hexahedra3D8() [6/7]

◆ Hexahedra3D8() [7/7]

◆ ~Hexahedra3D8()

Member Function Documentation

◆ Area()

◆ AverageEdgeLength()

◆ CalculateDistance()

◆ ComputeDihedralAngles()

◆ ComputeSolidAngles()

◆ Create() [1/2]

◆ Create() [2/2]

◆ DomainSize()

◆ EdgesNumber()

◆ FacesNumber()

◆ GenerateEdges()

◆ GenerateFaces()

◆ GetGeometryFamily()

◆ GetGeometryType()

◆ HasIntersection()

◆ Info()

◆ IsInside()

◆ KRATOS_CLASS_POINTER_DEFINITION()

◆ Length()

◆ MaxDihedralAngle()

◆ MaxEdgeLength()

◆ MinDihedralAngle()

◆ MinEdgeLength()

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ PointsLocalCoordinates()

◆ PrintData()

◆ PrintInfo()

◆ ShapeFunctionsLocalGradients()

◆ ShapeFunctionsSecondDerivatives()

◆ ShapeFunctionsValues()

◆ ShapeFunctionValue()

◆ ShortestToLongestEdgeQuality()

◆ Volume()

◆ VolumeToRMSEdgeLength()

Friends And Related Function Documentation

◆ Hexahedra3D8

◆ Serializer

template<class TPointType>
class Kratos::Hexahedra3D8< TPointType >