#include <math_utilities.hpp>

Collaboration diagram for Kratos::GeoMechanicsMathUtilities< TDataType >:

Public Types
type definitions
typedef Matrix	MatrixType

typedef Vector	VectorType

typedef unsigned int	IndexType

typedef unsigned int	SizeType

typedef MathUtils< TDataType >	MathUtilsType

typedef DenseVector< Vector >	Second_Order_Tensor

typedef DenseVector< Second_Order_Tensor >	Third_Order_Tensor

typedef DenseVector< DenseVector< Matrix > >	Fourth_Order_Tensor

typedef matrix< Second_Order_Tensor >	Matrix_Second_Tensor

Static Public Member Functions
static bool	CardanoFormula (double a, double b, double c, double d, Vector &solution)

static Vector	EigenValues (const Matrix &A, double tolerance, double zero)

static Vector	EigenValuesDirectMethod (const Matrix &A)

static void	QRFactorization (const MatrixType &A, MatrixType &Q, MatrixType &R)

static void	EigenVectors (const MatrixType &A, MatrixType &vectors, VectorType &lambda, double zero_tolerance=1e-9, int max_iterations=10)

static MatrixType	StrainVectorToTensor (const VectorType &Strains)

static Vector	TensorToStrainVector (const Matrix &Tensor)

static double	NormTensor (Matrix &Tensor)

static void	VectorToTensor (const Vector &Stress, Matrix &Tensor)

static void	TensorToVector (const Matrix &Tensor, Vector &Vector)

static void	TensorToMatrix (Fourth_Order_Tensor &Tensor, Matrix &Matrix)

static void	MatrixToTensor (MatrixType &A, std::vector< std::vector< Matrix > > &Tensor)

static void	MatrixToTensor (MatrixType &A, array_1d< double, 81 > &Tensor)

static void	TensorToMatrix (std::vector< std::vector< Matrix > > &Tensor, Matrix &Matrix)

static void	TensorToMatrix (const array_1d< double, 81 > &Tensor, Matrix &Matrix)

static void	DeviatoricUnity (std::vector< std::vector< Matrix > > &Unity)

static void	DeviatoricUnity (array_1d< double, 81 > &Unity)

static bool	Clipping (std::vector< Point * > &clipping_points, std::vector< Point * > &subjected_points, std::vector< Point * > &result_points, double tolerance)

Member Typedef Documentation

◆ Fourth_Order_Tensor

template<class TDataType >

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

◆ IndexType

template<class TDataType >

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

◆ MathUtilsType

template<class TDataType >

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

◆ Matrix_Second_Tensor

template<class TDataType >

typedef matrix<Second_Order_Tensor> Kratos::GeoMechanicsMathUtilities< TDataType >::Matrix_Second_Tensor

◆ MatrixType

template<class TDataType >

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

◆ Second_Order_Tensor

template<class TDataType >

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

◆ SizeType

template<class TDataType >

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

◆ Third_Order_Tensor

template<class TDataType >

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

◆ VectorType

template<class TDataType >

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

Member Function Documentation

◆ CardanoFormula()

template<class TDataType >

static bool Kratos::GeoMechanicsMathUtilities< TDataType >::CardanoFormula	(	double	a,
		double	b,
		double	c,
		double	d,
		Vector &	solution
	)

inlinestatic

calculates the solutions for a given cubic polynomial equation 0= a*x^3+b*x^2+c*x+d

Parameters

a	coefficient
b	coefficient
c	coefficient
d	coefficient
ZeroTol	number treated as zero

Returns: Vector of solutions WARNING only valid cubic (not quadratic, not linear, not constant) equations with three real (not complex) solutions

◆ Clipping()

template<class TDataType >

static bool Kratos::GeoMechanicsMathUtilities< TDataType >::Clipping	(	std::vector< Point * > &	clipping_points,
		std::vector< Point * > &	subjected_points,
		std::vector< Point * > &	result_points,
		double	tolerance
	)

inlinestatic

Performs clipping on the two polygons clipping_points and subjected_points (the technique used is Sutherland-Hodgman clipping) and returns the overlapping polygon result_points. The method works in 3D. Both polygons have to be convex, but they can be slightly perturbated in 3D space, this allows for performing clipping on two interpolated interfaces

Parameters

clipping_points	vertices of clipping polygon
subjected_points	vertices of subjected polygon
result_points	vertices of overlapping polygon

Returns: false= no overlapping polygon, true= overlapping polygon found

◆ DeviatoricUnity() [1/2]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::DeviatoricUnity ( array_1d< double, 81 > & Unity )

inlinestatic

Generates the fourth order deviatoric unity tensor

Parameters

Unity the deviatoric unity (will be overwritten)

◆ DeviatoricUnity() [2/2]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::DeviatoricUnity ( std::vector< std::vector< Matrix > > & Unity )

inlinestatic

Generates the fourth order deviatoric unity tensor

Parameters

Unity the deviatoric unity (will be overwritten)

◆ EigenValues()

template<class TDataType >

static Vector Kratos::GeoMechanicsMathUtilities< TDataType >::EigenValues	(	const Matrix &	A,
		double	tolerance,
		double	zero
	)

inlinestatic

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

Parameters

A	the given square matrix the eigenvalues are to be calculated.
tolerance	convergence criteria
zero	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::GeoMechanicsMathUtilities< TDataType >::EigenValuesDirectMethod ( const Matrix & A )

inlinestatic

calculates the eigenvectiors using a direct method.

Parameters

A	the given square matrix the eigenvalues are to be calculated. WARNING only valid symmetric 3*3 Matrices

◆ EigenVectors()

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::EigenVectors	(	const MatrixType &	A,
		MatrixType &	vectors,
		VectorType &	lambda,
		double	zero_tolerance = `1e-9`,
		int	max_iterations = `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

A	the given symmetric matrix where the eigenvectors have to be calculated.
vectors	where the eigenvectors will be stored
lambda	wher the eigenvalues will be stored
zero_tolerance	the largest value considered to be zero
max_iterations	allowed

◆ MatrixToTensor() [1/2]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::MatrixToTensor	(	MatrixType &	A,
		array_1d< double, 81 > &	Tensor
	)

inlinestatic

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

Parameters

Tensor	the given Matrix
Vector	the Tensor

◆ MatrixToTensor() [2/2]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::MatrixToTensor	(	MatrixType &	A,
		std::vector< std::vector< Matrix > > &	Tensor
	)

inlinestatic

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

Parameters

Tensor	the given Matrix
Vector	the Tensor

◆ NormTensor()

template<class TDataType >

static double Kratos::GeoMechanicsMathUtilities< TDataType >::NormTensor ( Matrix & Tensor )

inlinestatic

Builds the norm of a gibven second order tensor

Parameters

Tensor the given second order tensor

Returns: the norm of the given tensor

◆ QRFactorization()

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< 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

A	the given square matrix the factorization is to be calculated.
Q	the result matrix Q
R	the result matrix R

◆ StrainVectorToTensor()

template<class TDataType >

static MatrixType Kratos::GeoMechanicsMathUtilities< TDataType >::StrainVectorToTensor ( const VectorType & Strains )

inlinestatic

calculates Eigenvectors and the EigenValues of given square matrix A(3x3) The QR Algorithm with shifts is used

Parameters

A	the given symmetric 3x3 real matrix
V	matrix to store the eigenvectors in rows
d	matrix to store the eigenvalues converts a strain vector into a matrix. Strains are assumed to be stored in the following way: \( [ e11, e22, e33, 2e12, 2e23, 2e13 ] \) for 3D case and \( [ e11, e22, 2e12 ] \) fir 2D case. Hence the deviatoric components of the strain vector are divided by 2 while they are stored into the matrix
Strains	the given strain vector

Returns: the corresponding strain tensor in matrix form

◆ TensorToMatrix() [1/3]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::TensorToMatrix	(	const array_1d< double, 81 > &	Tensor,
		Matrix &	Matrix
	)

inlinestatic

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

Parameters

Tensor	the given Tensor
Vector	the Matrix

◆ TensorToMatrix() [2/3]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::TensorToMatrix	(	Fourth_Order_Tensor &	Tensor,
		Matrix &	Matrix
	)

inlinestatic

◆ TensorToMatrix() [3/3]

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::TensorToMatrix	(	std::vector< std::vector< Matrix > > &	Tensor,
		Matrix &	Matrix
	)

inlinestatic

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

Parameters

Tensor	the given Tensor
Vector	the Matrix

◆ TensorToStrainVector()

template<class TDataType >

static Vector Kratos::GeoMechanicsMathUtilities< TDataType >::TensorToStrainVector ( const Matrix & Tensor )

inlinestatic

◆ TensorToVector()

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::TensorToVector	(	const Matrix &	Tensor,
		Vector &	Vector
	)

inlinestatic

Transforms a given symmetric Tensor of second order (3*3) to a corresponing 6*1 Vector

Parameters

Tensor	the given symmetric second order tensor
Vector	the vector

◆ VectorToTensor()

template<class TDataType >

static void Kratos::GeoMechanicsMathUtilities< TDataType >::VectorToTensor	(	const Vector &	Stress,
		Matrix &	Tensor
	)

inlinestatic

Transforms a given 6*1 Vector to a corresponing symmetric Tensor of second order (3*3)

Parameters

Vector	the given vector
Tensor	the symmetric second order tensor

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

/home/runner/work/Documentation/Documentation/master/applications/GeoMechanicsApplication/custom_utilities/math_utilities.hpp

Public Types

Static Public Member Functions

Member Typedef Documentation

◆ Fourth_Order_Tensor

◆ IndexType

◆ MathUtilsType

◆ Matrix_Second_Tensor

◆ MatrixType

◆ Second_Order_Tensor

◆ SizeType

◆ Third_Order_Tensor

◆ VectorType

Member Function Documentation

◆ CardanoFormula()

◆ Clipping()

◆ DeviatoricUnity() [1/2]

◆ DeviatoricUnity() [2/2]

◆ EigenValues()

◆ EigenValuesDirectMethod()

◆ EigenVectors()

◆ MatrixToTensor() [1/2]

◆ MatrixToTensor() [2/2]

◆ NormTensor()

◆ QRFactorization()

◆ StrainVectorToTensor()

◆ TensorToMatrix() [1/3]

◆ TensorToMatrix() [2/3]

◆ TensorToMatrix() [3/3]

◆ TensorToStrainVector()

◆ TensorToVector()

◆ VectorToTensor()