#include <particle_mechanics_math_utilities.h>

Collaboration diagram for Kratos::ParticleMechanicsMathUtilities< TDataType >:

type definitions
typedef Matrix	MatrixType

typedef Vector	VectorType

typedef unsigned int	IndexType

typedef unsigned int	SizeType

typedef MathUtils< TDataType >	MathUtilsType

typedef Node	NodeType

typedef Geometry< Node >	GeometryType

typedef DenseVector< Vector >	Second_Order_Tensor

typedef DenseVector< Second_Order_Tensor >	Third_Order_Tensor

typedef DenseVector< DenseVector< Matrix > >	Fourth_Order_Tensor

typedef DenseMatrix< Second_Order_Tensor >	Matrix_Second_Tensor

static void	GetRotationMatrix (MatrixType &rRotationMatrix, const VectorType &rNormalVector, const unsigned int Dimension)

static double	CalculateRadius (const Matrix &rN, GeometryType &Geom, const Configuration ThisConfiguration=Current, const IndexType IntegrationPointIndex=0)

static double	CalculateRadiusPoint (GeometryType &Geom, const Configuration ThisConfiguration=Current)

static void	QRFactorization (const MatrixType &A, MatrixType &Q, MatrixType &R)
	Calculates the QR Factorization of given square matrix A=QR. The Factorization is performed using the householder algorithm. More...

static Vector	EigenValues (const Matrix &A, const double rTolerance=1e-9, const double rZeroTolerance=1e-9)
	Calculates Eigenvalues of given square matrix A. The QR Algorithm with shifts is used. More...

static Vector	EigenValuesDirectMethod (const Matrix &A)
	Calculates the Eigenvalues using a direct method. More...

static void	EigenVectors (const MatrixType &A, MatrixType &rEigenVectors, VectorType &rEigenValues, const double rZeroTolerance=1e-9, const unsigned int rMaxIteration=10)
	Calculates the Eigenvectors and Eigenvalues of given symmetric matrix A. The eigenvectors and eigenvalues are calculated using the iterative Gauss-Seidel-method. More...

template<class TVectorType >
static void	Normalize (TVectorType &v)
	Normalises a vector. Vector is scaled by \( V_{norm} = \frac{V}{\|V\|} \). More...

static double	NormTensor (Matrix &rTensor)
	Builds the norm of a given second order tensor. More...

static void	TensorToMatrix (const Fourth_Order_Tensor &rTensor, Matrix &rMatrix)
	Transforms a given fourth order tensor to a corresponing Matrix. More...

static void	MatrixToTensor (const MatrixType &A, std::vector< std::vector< Matrix > > &rTensor)
	Transforms a given 6*6 Matrix to a corresponing 4th order tensor. More...

static void	MatrixToTensor (const MatrixType &A, array_1d< double, 81 > &rTensor)
	Transforms a given 6*6 Matrix to a corresponing 4th order tensor. More...

static void	TensorToMatrix (const std::vector< std::vector< Matrix > > &rTensor, Matrix &rMatrix)
	Transforms a given 4th order tensor to a corresponing 6*6 Matrix. More...

static void	TensorToMatrix (const array_1d< double, 81 > &rTensor, Matrix &rMatrix)
	Transforms a given 4th order Tensor to a corresponing 6*6 Matrix. More...

Member Typedef Documentation

◆ Fourth_Order_Tensor

template<class TDataType >

typedef DenseVector<DenseVector<Matrix> > Kratos::ParticleMechanicsMathUtilities< TDataType >::Fourth_Order_Tensor

◆ GeometryType

template<class TDataType >

typedef Geometry< Node > Kratos::ParticleMechanicsMathUtilities< TDataType >::GeometryType

◆ IndexType

template<class TDataType >

typedef unsigned int Kratos::ParticleMechanicsMathUtilities< TDataType >::IndexType

◆ MathUtilsType

template<class TDataType >

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

◆ Matrix_Second_Tensor

template<class TDataType >

typedef DenseMatrix<Second_Order_Tensor> Kratos::ParticleMechanicsMathUtilities< TDataType >::Matrix_Second_Tensor

◆ MatrixType

template<class TDataType >

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

◆ NodeType

template<class TDataType >

typedef Node Kratos::ParticleMechanicsMathUtilities< TDataType >::NodeType

◆ Second_Order_Tensor

template<class TDataType >

typedef DenseVector<Vector> Kratos::ParticleMechanicsMathUtilities< TDataType >::Second_Order_Tensor

◆ SizeType

template<class TDataType >

typedef unsigned int Kratos::ParticleMechanicsMathUtilities< TDataType >::SizeType

◆ Third_Order_Tensor

template<class TDataType >

typedef DenseVector<Second_Order_Tensor> Kratos::ParticleMechanicsMathUtilities< TDataType >::Third_Order_Tensor

◆ VectorType

template<class TDataType >

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

Member Function Documentation

◆ CalculateRadius()

template<class TDataType >

static double Kratos::ParticleMechanicsMathUtilities< TDataType >::CalculateRadius	(	const Matrix &	rN,
		GeometryType &	Geom,
		const Configuration	ThisConfiguration = `Current`,
		const IndexType	IntegrationPointIndex = `0`
	)

inlinestatic

Calculates the radius of axisymmetry

Parameters

N	The Gauss Point shape function
Geom	The geometry studied

Returns: Radius: The radius of axisymmetry

◆ CalculateRadiusPoint()

template<class TDataType >

static double Kratos::ParticleMechanicsMathUtilities< TDataType >::CalculateRadiusPoint	(	GeometryType &	Geom,
		const Configuration	ThisConfiguration = `Current`
	)

inlinestatic

Calculates the radius of axisymmetry for a point

Parameters

Geom	The geometry studied

Returns: The radius of axisymmetry

◆ EigenValues()

template<class TDataType >

static Vector Kratos::ParticleMechanicsMathUtilities< TDataType >::EigenValues	(	const Matrix &	A,
		const double	rTolerance = `1e-9`,
		const double	rZeroTolerance = `1e-9`
	)

inlinestatic

Calculates Eigenvalues of given square matrix A. The QR Algorithm with shifts is used.

Parameters

[in]	A	the given square matrix the eigenvalues are to be calculated.
[in]	rTolerance	convergence criteria.
[in]	rZeroTolerance	number treated as zero.

Returns: Vector of eigenvalues.

Warning: Only valid for 2*2 and 3*3 Matrices yet.

◆ EigenValuesDirectMethod()

template<class TDataType >

static Vector Kratos::ParticleMechanicsMathUtilities< TDataType >::EigenValuesDirectMethod ( const Matrix & A )

inlinestatic

Calculates the Eigenvalues using a direct method.

Parameters

A	the given square matrix the eigenvalues are to be calculated.

Returns: Vector of eigenvalues.

Warning: only valid symmetric 3*3 Matrices.

◆ EigenVectors()

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::EigenVectors	(	const MatrixType &	A,
		MatrixType &	rEigenVectors,
		VectorType &	rEigenValues,
		const double	rZeroTolerance = `1e-9`,
		const unsigned int	rMaxIteration = `10`
	)

inlinestatic

Calculates the Eigenvectors and Eigenvalues of given symmetric matrix A. The eigenvectors and eigenvalues are calculated using the iterative Gauss-Seidel-method.

Parameters

[in]	A	the given symmetric matrix where the eigenvectors have to be calculated.
[out]	rEigenVectors	Where the eigenvectors will be stored.
[out]	rEigenValues	Where the eigenvalues will be stored.
[in]	rZeroTolerance	The largest value considered to be zero.
[in]	rMaxIteration	Maximum number of iteration allowed.

◆ GetRotationMatrix()

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::GetRotationMatrix	(	MatrixType &	rRotationMatrix,
		const VectorType &	rNormalVector,
		const unsigned int	Dimension
	)

inlinestatic

This function returns rotation matrix from given normal vector and dimension

Parameters

rRotationMatrix	Rotation Matrix
rNormalVector	Normal Vector at the material point condition
Dimension	given dimension

◆ MatrixToTensor() [1/2]

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::MatrixToTensor	(	const MatrixType &	A,
		array_1d< double, 81 > &	rTensor
	)

inlinestatic

Transforms a given 6*6 Matrix to a corresponing 4th order tensor.

Parameters

[in]	rTensor	the given Matrix
[out]	rTensor	the rTensor

◆ MatrixToTensor() [2/2]

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::MatrixToTensor	(	const MatrixType &	A,
		std::vector< std::vector< Matrix > > &	rTensor
	)

inlinestatic

Transforms a given 6*6 Matrix to a corresponing 4th order tensor.

Parameters

[in]	rTensor	the given Matrix
[out]	rTensor	the rTensor

◆ Normalize()

template<class TDataType >

template<class TVectorType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::Normalize ( TVectorType & v )

inlinestatic

Normalises a vector. Vector is scaled by \( V_{norm} = \frac{V}{|V|} \).

Parameters

[in/out] v Vector to be normalized

◆ NormTensor()

template<class TDataType >

static double Kratos::ParticleMechanicsMathUtilities< TDataType >::NormTensor ( Matrix & rTensor )

inlinestatic

Builds the norm of a given second order tensor.

Parameters

[in] rTensor the given second order tensor

Returns: The norm of the given tensor

◆ QRFactorization()

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::QRFactorization	(	const MatrixType &	A,
		MatrixType &	Q,
		MatrixType &	R
	)

inlinestatic

Calculates the QR Factorization of given square matrix A=QR. The Factorization is performed using the householder algorithm.

Parameters

[in]	A	The given square matrix the factorization is to be calculated.
[out]	Q	The result matrix Q.
[out]	R	The result matrix R.

◆ TensorToMatrix() [1/3]

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::TensorToMatrix	(	const array_1d< double, 81 > &	rTensor,
		Matrix &	rMatrix
	)

inlinestatic

Transforms a given 4th order Tensor to a corresponing 6*6 Matrix.

Parameters

[in]	rTensor	the given Tensor
[out]	Matrix	the Matrix

◆ TensorToMatrix() [2/3]

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::TensorToMatrix	(	const Fourth_Order_Tensor &	rTensor,
		Matrix &	rMatrix
	)

inlinestatic

Transforms a given fourth order tensor to a corresponing Matrix.

Parameters

[in]	rTensor	the given symmetric second order tensor
[out]	rVector	the vector

◆ TensorToMatrix() [3/3]

template<class TDataType >

static void Kratos::ParticleMechanicsMathUtilities< TDataType >::TensorToMatrix	(	const std::vector< std::vector< Matrix > > &	rTensor,
		Matrix &	rMatrix
	)

inlinestatic

Transforms a given 4th order tensor to a corresponing 6*6 Matrix.

Parameters

[in]	rTensor	the given Tensor
[out]	rMatrix	the Matrix

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

/home/runner/work/Documentation/Documentation/master/applications/ParticleMechanicsApplication/custom_utilities/particle_mechanics_math_utilities.h

type definitions

Member Typedef Documentation

◆ Fourth_Order_Tensor

◆ GeometryType

◆ IndexType

◆ MathUtilsType

◆ Matrix_Second_Tensor

◆ MatrixType

◆ NodeType

◆ Second_Order_Tensor

◆ SizeType

◆ Third_Order_Tensor

◆ VectorType

Member Function Documentation

◆ CalculateRadius()

◆ CalculateRadiusPoint()

◆ EigenValues()

◆ EigenValuesDirectMethod()

◆ EigenVectors()

◆ GetRotationMatrix()

◆ MatrixToTensor() [1/2]

◆ MatrixToTensor() [2/2]

◆ Normalize()

◆ NormTensor()

◆ QRFactorization()

◆ TensorToMatrix() [1/3]

◆ TensorToMatrix() [2/3]

◆ TensorToMatrix() [3/3]