#include <beam_math_utilities.hpp>

Collaboration diagram for Kratos::BeamMathUtils< TDataType >:

Public Types

typedef Matrix	MatrixType

typedef Vector	VectorType

typedef Quaternion< double >	QuaternionType

typedef MathUtils< TDataType >	MathUtilsType

typedef BeamMathUtils< TDataType >	BeamMathUtilsType

Static Public Member Functions

template<class TVector3 >
static TVector3 &	MapToCurrentLocalFrame (QuaternionType &rQuaternion, TVector3 &rVector)

template<class TVector3 >
static TVector3 &	MapToReferenceLocalFrame (QuaternionType &rQuaternion, TVector3 &rVector)

template<class TVector3 >
static void	ExponentialTransform (const TVector3 &rVector, MatrixType &rExponentialTensor)

template<class TVector3 >
static void	InverseExponentialTransform (const MatrixType &rExponentialTensor, TVector3 &rVector)

template<class TVector3 >
static void	CayleyTransform (const TVector3 &rVector, MatrixType &rCayleyTensor)

template<class TVector3 >
static void	InverseCayleyTransform (const MatrixType &rCayleyTensor, TVector3 &rVector)

template<class TVector3 , class TMatrix3 >
static void	VectorToSkewSymmetricTensor (const TVector3 &rVector, TMatrix3 &rSkewSymmetricTensor)

template<class TMatrix3 , class TVector3 >
static void	SkewSymmetricTensorToVector (const TMatrix3 &rSkewSymmetricTensor, TVector3 &rVector)

static double	KroneckerDelta (int i, int j)

static double	LeviCivitaEpsilon (int i, int j, int k)

static void	AddVector (const VectorType &rInputVector, VectorType &rOutputVector, const unsigned int InitialRow)

static void	SubstractVector (const VectorType &rInputVector, VectorType &rOutputVector, const unsigned int InitialRow)

template<class TMatrix , class TInputMatrix >
static void	AddMatrix (TMatrix &rDestination, const TInputMatrix &rInputMatrix, const unsigned int rInitialRow, const unsigned int rInitialCol)

template<class TMatrix , class TInputMatrix >
static void	SubtractMatrix (TMatrix &rDestination, const TInputMatrix &rInputMatrix, const unsigned int rInitialRow, const unsigned int rInitialCol)

static void	MapLocalToGlobal2D (const QuaternionType &rLocalToGlobalQuaternion, MatrixType &rMatrix)

static void	MapLocalToGlobal2D (const QuaternionType &rLocalToGlobalQuaternion, VectorType &rVector)

static void	MapLocalToGlobal2D (const MatrixType &rLocalToGlobalMatrix, MatrixType &rMatrix)

static void	MapLocalToGlobal2D (const MatrixType &rLocalToGlobalMatrix, VectorType &rVector)

static void	MapLocalToGlobal3D (const QuaternionType &rLocalToGlobalQuaternion, MatrixType &rMatrix)

static void	MapLocalToGlobal3D (const QuaternionType &rLocalToGlobalQuaternion, VectorType &rVector)

static void	MapLocalToGlobal3D (const MatrixType &rLocalToGlobalMatrix, MatrixType &rMatrix)

static void	MapLocalToGlobal3D (const MatrixType &rLocalToGlobalMatrix, VectorType &rVector)

template<class TVector3 >
static void	CalculateLocalAxesMatrix (const TVector3 &rLocalX, MatrixType &rRotationMatrix)

template<class TVector3 >
static void	CalculateLocalAxesVectors (TVector3 &rLocalX, TVector3 &rLocalY, TVector3 &rLocalZ)

template<class TVector3 >
static void	CalculateLocalAxesMatrix (const TVector3 &rLocalX, const TVector3 &rLocalY, MatrixType &rRotationMatrix)

template<class TVector3 >
static void	CalculateLocalAxisVector (TVector3 &rLocalX, TVector3 &rLocalY, TVector3 &rLocalZ)

static bool	CheckOrthogonality (const Matrix &rTensor, const std::string &Name, bool Verbose)

Member Typedef Documentation

◆ BeamMathUtilsType

template<class TDataType >

typedef BeamMathUtils<TDataType> Kratos::BeamMathUtils< TDataType >::BeamMathUtilsType

◆ MathUtilsType

template<class TDataType >

typedef MathUtils<TDataType> Kratos::BeamMathUtils< TDataType >::MathUtilsType

◆ MatrixType

template<class TDataType >

typedef Matrix Kratos::BeamMathUtils< TDataType >::MatrixType

name Type Definitions

◆ QuaternionType

template<class TDataType >

typedef Quaternion<double> Kratos::BeamMathUtils< TDataType >::QuaternionType

◆ VectorType

template<class TDataType >

typedef Vector Kratos::BeamMathUtils< TDataType >::VectorType

Member Function Documentation

◆ AddMatrix()

template<class TDataType >

template<class TMatrix , class TInputMatrix >

static void Kratos::BeamMathUtils< TDataType >::AddMatrix	(	TMatrix &	rDestination,
		const TInputMatrix &	rInputMatrix,
		const unsigned int	rInitialRow,
		const unsigned int	rInitialCol
	)

inlinestatic

"InputMatrix" is ADDED to "Destination" matrix starting from InitialRow and InitialCol of the destination matrix "Destination" is assumed to be able to contain the "input matrix" (no check is performed on the bounds)

Returns: rDestination: The matric destination

Parameters

rInputMatrix	The input matrix to be computed
rInitialRow	The initial row to compute
rInitialCol	The initial column to compute

◆ AddVector()

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::AddVector	(	const VectorType &	rInputVector,
		VectorType &	rOutputVector,
		const unsigned int	InitialRow
	)

inlinestatic

Add a Nodal vector to a Elemental vector

Parameters

rInputVector	LocalNodalVector (input parameter)
rOutputVector	LocalElementalVector (output parameter)
InitialRow	InitialRowNumber, initial index of the OutputVector note the initialization of the outputvector must be done previously to the call of the method

◆ CalculateLocalAxesMatrix() [1/2]

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::CalculateLocalAxesMatrix	(	const TVector3 &	rLocalX,
		const TVector3 &	rLocalY,
		MatrixType &	rRotationMatrix
	)

inlinestatic

Deffault expression for GID local beam axes:: E1 is considered the local beam axial direction

Parameters

rLocalX	Local Beam axis vector (input parameter)
rLocalY	Local axis 2 vector (input parameter)
rRotationMatrix	transformation matrix from local to global frame (output parameter)

◆ CalculateLocalAxesMatrix() [2/2]

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::CalculateLocalAxesMatrix	(	const TVector3 &	rLocalX,
		MatrixType &	rRotationMatrix
	)

inlinestatic

Deffault expression for GID local beam axes:: E1 is considered the local beam axial direction

Parameters

rLocalX	Local Beam axis vector (input parameter)
rRotationMatrix	transformation matrix from local to global frame (output parameter)

◆ CalculateLocalAxesVectors()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::CalculateLocalAxesVectors	(	TVector3 &	rLocalX,
		TVector3 &	rLocalY,
		TVector3 &	rLocalZ
	)

inlinestatic

Deffault expression for GID local beam axes:: E1 is considered the local beam axial direction

Parameters

rLocalX	Local Beam axis director vector E1 (input parameter) (output parameter)
rLocalY	Local Beam axis director vector E2 (output parameter)
rLocalZ	Local Beam axis director vector E3 (output parameter)

◆ CalculateLocalAxisVector()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::CalculateLocalAxisVector	(	TVector3 &	rLocalX,
		TVector3 &	rLocalY,
		TVector3 &	rLocalZ
	)

inlinestatic

Deffault expression for GID local beam axes:: E1 is considered the local beam axial direction

Parameters

rLocalX	Local Beam axis director vector E1 (input parameter) (output parameter)
rLocalY	Local Beam axis director vector E2 (input parameter) (output parameter)
rLocalZ	Local Beam axis director vector E3 (output parameter)

◆ CayleyTransform()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::CayleyTransform	(	const TVector3 &	rVector,
		MatrixType &	rCayleyTensor
	)

inlinestatic

Transform a rotation vector to a rotation matrix with the Cayley transform

Parameters

rVector	rotation vector (input parameter)
rCayleyTensor	rotation matrix (output parameter)

◆ CheckOrthogonality()

template<class TDataType >

static bool Kratos::BeamMathUtils< TDataType >::CheckOrthogonality	(	const Matrix &	rTensor,
		const std::string &	Name,
		bool	Verbose
	)

inlinestatic

Check if a Tensor is orthogonal

Parameters

rTensor	transformation matrix to be checked
Name	Name of the checked tensor to be verbosed
Verbose	Set verbosity for the check

◆ ExponentialTransform()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::ExponentialTransform	(	const TVector3 &	rVector,
		MatrixType &	rExponentialTensor
	)

inlinestatic

Transform a rotation vector to a rotation matrix with the Exponential transform

Parameters

rVector	rotation vector (input parameter)
rExponentialTensor	rotation matrix (output parameter)

◆ InverseCayleyTransform()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::InverseCayleyTransform	(	const MatrixType &	rCayleyTensor,
		TVector3 &	rVector
	)

inlinestatic

Transform a rotation tensor to a rotation vector with the inverse of the Cayley transform

Parameters

rCayleyTensor	rotation matrix (input parameter)
rVector	rotation vector (output parameter)

◆ InverseExponentialTransform()

template<class TDataType >

template<class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::InverseExponentialTransform	(	const MatrixType &	rExponentialTensor,
		TVector3 &	rVector
	)

inlinestatic

Transform a rotation matrix to a rotation vector with the inverse of the Exponential transform

Parameters

rCayleyTensor	rotation matrix (input parameter)
rVector	rotation vector (output parameter)

◆ KroneckerDelta()

template<class TDataType >

static double Kratos::BeamMathUtils< TDataType >::KroneckerDelta	(	int	i,
		int	j
	)

inlinestatic

Get kroneckrDelta :: two order tensor that gives the value of the identity

Parameters

i	coefficient i
j	coefficient j Returns a double with the value

◆ LeviCivitaEpsilon()

template<class TDataType >

static double Kratos::BeamMathUtils< TDataType >::LeviCivitaEpsilon	(	int	i,
		int	j,
		int	k
	)

inlinestatic

Get Levi Civita Epsilon :: third order tensor that gives the value of a vectorial product

Parameters

i	coefficient i
j	coefficient j
k	coefficient k Returns a double with the sign

◆ MapLocalToGlobal2D() [1/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal2D	(	const MatrixType &	rLocalToGlobalMatrix,
		MatrixType &	rMatrix
	)

inlinestatic

Map a Matrix expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalMatrix	transformation matrix from local to global frame
rMatrix	matrix to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method return value : A = Q * A' * QT

◆ MapLocalToGlobal2D() [2/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal2D	(	const MatrixType &	rLocalToGlobalMatrix,
		VectorType &	rVector
	)

inlinestatic

Map a Vector expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalMatrix	transformation matrix from local to global frame
rVector	vector to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method

◆ MapLocalToGlobal2D() [3/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal2D	(	const QuaternionType &	rLocalToGlobalQuaternion,
		MatrixType &	rMatrix
	)

inlinestatic

Map a Matrix expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalQuaternion	transformation quaternion from local to global frame
rMatrix	matrix to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method return value : A = Q * A' * QT

◆ MapLocalToGlobal2D() [4/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal2D	(	const QuaternionType &	rLocalToGlobalQuaternion,
		VectorType &	rVector
	)

inlinestatic

Map a Vector expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalQuaternion	transformation quaternion from local to global frame
rVector	vector to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method

◆ MapLocalToGlobal3D() [1/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal3D	(	const MatrixType &	rLocalToGlobalMatrix,
		MatrixType &	rMatrix
	)

inlinestatic

Map a Matrix expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalMatrix	transformation matrix from local to global frame
rMatrix	matrix to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method return value : A = Q * A' * QT

◆ MapLocalToGlobal3D() [2/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal3D	(	const MatrixType &	rLocalToGlobalMatrix,
		VectorType &	rVector
	)

inlinestatic

Map a Vector expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalMatrix	transformation matrix from local to global frame
rVector	vector to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method

◆ MapLocalToGlobal3D() [3/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal3D	(	const QuaternionType &	rLocalToGlobalQuaternion,
		MatrixType &	rMatrix
	)

inlinestatic

Map a Matrix expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalQuaternion	transformation quaternion from local to global frame
rMatrix	matrix to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method return value : A = Q * A' * QT

◆ MapLocalToGlobal3D() [4/4]

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::MapLocalToGlobal3D	(	const QuaternionType &	rLocalToGlobalQuaternion,
		VectorType &	rVector
	)

inlinestatic

Map a Vector expressed on the Local frame of an element to a Global frame expression

Parameters

rLocalToGlobalQuaternion	transformation quaternion from local to global frame
rVector	vector to be transformed (output parameter) note the initialization of the Matrices must be done previously to the call of the method

◆ MapToCurrentLocalFrame()

template<class TDataType >

template<class TVector3 >

static TVector3& Kratos::BeamMathUtils< TDataType >::MapToCurrentLocalFrame	(	QuaternionType &	rQuaternion,
		TVector3 &	rVector
	)

inlinestatic

name Math Utilities for beams Transform a vector from the reference to the current local frame (MATERIAL frame for a beam)

Parameters

rQuaternion	Quaternion representing the rotation from the reference to the current local frames
rVector	Vector to be rotated the rotated vector rVector is returned.

◆ MapToReferenceLocalFrame()

template<class TDataType >

template<class TVector3 >

static TVector3& Kratos::BeamMathUtils< TDataType >::MapToReferenceLocalFrame	(	QuaternionType &	rQuaternion,
		TVector3 &	rVector
	)

inlinestatic

Transform a vector from the current to the reference local frame (SPATIAL frame for a beam)

Parameters

rQuaternion	Quaternion representing the rotation from the reference to the current local frames
rVector	Vector to be rotated the rotated vector rVariable is returned.

◆ SkewSymmetricTensorToVector()

template<class TDataType >

template<class TMatrix3 , class TVector3 >

static void Kratos::BeamMathUtils< TDataType >::SkewSymmetricTensorToVector	(	const TMatrix3 &	rSkewSymmetricTensor,
		TVector3 &	rVector
	)

inlinestatic

Transform a skew symmetric matrix to a rotation vector

Parameters

rSkewSymmetricTensor	skew symmetric matrix (input parameter)
rVector	rotation vector (output parameter)

◆ SubstractVector()

template<class TDataType >

static void Kratos::BeamMathUtils< TDataType >::SubstractVector	(	const VectorType &	rInputVector,
		VectorType &	rOutputVector,
		const unsigned int	InitialRow
	)

inlinestatic

Substract a Nodal vector from an Elemental vector

Parameters

rInputVector	LocalNodalVector (input parameter)
rOutputVector	LocalElementalVector (output parameter)
InitialRow	InitialRowNumber, initial index of the OutputVector note the initialization of the outputvector must be done previously to the call of the method

◆ SubtractMatrix()

template<class TDataType >

template<class TMatrix , class TInputMatrix >

static void Kratos::BeamMathUtils< TDataType >::SubtractMatrix	(	TMatrix &	rDestination,
		const TInputMatrix &	rInputMatrix,
		const unsigned int	rInitialRow,
		const unsigned int	rInitialCol
	)

inlinestatic

"InputMatrix" is SUBTRACTED to "Destination" matrix starting from InitialRow and InitialCol of the destination matrix "Destination" is assumed to be able to contain the "input matrix" (no check is performed on the bounds)

Returns: rDestination: The matric destination

Parameters

rInputMatrix	The input matrix to be computed
rInitialRow	The initial row to compute
rInitialCol	The initial column to compute

◆ VectorToSkewSymmetricTensor()

template<class TDataType >

template<class TVector3 , class TMatrix3 >

static void Kratos::BeamMathUtils< TDataType >::VectorToSkewSymmetricTensor	(	const TVector3 &	rVector,
		TMatrix3 &	rSkewSymmetricTensor
	)

inlinestatic

Transform a rotation vector to a skew symmetric matrix

Parameters

rVector	rotation vector (input parameter)
rSkewSymmetricTensor	skew symmetric matrix (output parameter)

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

/home/runner/work/Documentation/Documentation/master/kratos/utilities/beam_math_utilities.hpp

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ BeamMathUtilsType

◆ MathUtilsType

◆ MatrixType

◆ QuaternionType

◆ VectorType

Member Function Documentation

◆ AddMatrix()

◆ AddVector()

◆ CalculateLocalAxesMatrix() [1/2]

◆ CalculateLocalAxesMatrix() [2/2]

◆ CalculateLocalAxesVectors()

◆ CalculateLocalAxisVector()

◆ CayleyTransform()

◆ CheckOrthogonality()

◆ ExponentialTransform()

◆ InverseCayleyTransform()

◆ InverseExponentialTransform()

◆ KroneckerDelta()

◆ LeviCivitaEpsilon()

◆ MapLocalToGlobal2D() [1/4]

◆ MapLocalToGlobal2D() [2/4]

◆ MapLocalToGlobal2D() [3/4]

◆ MapLocalToGlobal2D() [4/4]

◆ MapLocalToGlobal3D() [1/4]

◆ MapLocalToGlobal3D() [2/4]

◆ MapLocalToGlobal3D() [3/4]

◆ MapLocalToGlobal3D() [4/4]

◆ MapToCurrentLocalFrame()

◆ MapToReferenceLocalFrame()

◆ SkewSymmetricTensorToVector()

◆ SubstractVector()

◆ SubtractMatrix()

◆ VectorToSkewSymmetricTensor()