EICR Element Independent CoRotational formulation. More...

#include <ASDEICR.h>

Public Types
typedef std::size_t	size_t

typedef ASDVector3< double >	Vector3Type

typedef std::vector< Vector3Type >	NodeContainerType

typedef Vector	VectorType

typedef Matrix	MatrixType

typedef ASDQuaternion< double >	QuaternionType

Static Public Member Functions
template<class TVec , class TMat >
static void	Spin (const TVec &V, TMat &S)
	Computes the Spin of the input vector V, and saves the result into the output matrix S. More...

template<class TVec , class TMat >
static void	Spin_AtRow (const TVec &V, TMat &S, size_t row_index)
	Computes the Spin of the input vector V, and saves the result into the output matrix S, at the specified row index. More...

template<class TVec , class TMat >
static void	Spin_AtRow (const TVec &V, TMat &S, size_t vector_index, size_t matrix_row_index)
	Computes the Spin of the input vector V, from the specified index, and saves the result into the output matrix S, at the specified row index. More...

template<class TVec , class TMat >
static void	Spin (const TVec &V, TMat &S, double mult)
	Computes the Spin of the input vector V, and saves the result into the output matrix S. More...

template<class TVec , class TMat >
static void	Spin_AtRow (const TVec &V, TMat &S, double mult, size_t row_index)
	Computes the Spin of the input vector V, and saves the result into the output matrix S, at the specified row index. More...

template<class TVec , class TMat >
static void	Spin_AtRow (const TVec &V, TMat &S, double mult, size_t vector_index, size_t matrix_row_index)
	Computes the Spin of the input vector V, from the specified index, and saves the result into the output matrix S, at the specified row index. More...

static void	SetZero (size_t n, size_t m, MatrixType &I)
	Sets the input matrix to the zero matrix of requested size. More...

static void	SetIdentity (size_t n, MatrixType &I, double value=1.0)
	Sets the input matrix to the identity of requested size. More...

static void	GetBlock (const VectorType &A, size_t begin, size_t end, VectorType &B)
	Copies the block [begin:end[ from A to B. More...

static void	GetBlock (const MatrixType &A, size_t begin, size_t end, MatrixType &B)
	Copies the block [begin:end[ from A to B. More...

static void	SetBlock (MatrixType &A, size_t begin, size_t end, const MatrixType &B)
	Copies the block [begin:end[ from B to A. More...

static void	OuterProd (const VectorType &A, const VectorType &B, MatrixType &C)
	computes the outer product A x B, in C. More...

static void	Compute_Pt (size_t num_nodes, MatrixType &P)
	Computes the Translational Projector Matrix. More...

static void	Compute_S (const NodeContainerType &nodes, MatrixType &S)
	Computes the Spin Lever Matrix. More...

static void	Compute_H (const VectorType &displacements, MatrixType &H)
	Computes the Axial Vector Jacobian. More...

static void	Compute_L (const VectorType &displacements, const VectorType &forces, const MatrixType &H, MatrixType &L)
	Computes the Spin derivative of (Axial Vector Jacobian)^T contracted with the nodal moment vector. More...

Detailed Description

EICR Element Independent CoRotational formulation.

E.I.C.R. is a utility class containing static methods related to the Element Independent Corotational Formulation. This class implements methods that do not depend on the element type, and so they can be used by any implementation of a corotational coordinate transformation.

Member Function Documentation

◆ Compute_H()

static void XC::EICR::Compute_H	(	const VectorType &	displacements,
		MatrixType &	H
	)

inlinestatic

Computes the Axial Vector Jacobian.

The output is a square matrix of size displacements.size() (which is num_nodes * 6). Note that 6 Degrees Of Freedom are assumed for each node.

Parameters

displacements the vector of nodal displacements and rotations in the local corotational coordinate system. (assumed size = num_nodes*6)

Returns: the H matrix

◆ Compute_L()

static void XC::EICR::Compute_L	(	const VectorType &	displacements,
		const VectorType &	forces,
		const MatrixType &	H,
		MatrixType &	L
	)

inlinestatic

Computes the Spin derivative of (Axial Vector Jacobian)^T contracted with the nodal moment vector.

The output is a square matrix of size displacements.size() (which is num_nodes * 6). Note that 6 Degrees Of Freedom are assumed for each node.

Parameters

displacements	the vector of nodal displacements and rotations in the local corotational coordinate system. (assumed size = num_nodes*6)
forces	the vector of nodal forces and moments in the local corotational coordinate system. (assumed size = num_nodes*6)
H	the Axial Vector Jacobian Matrix computed with a previous call to EICR::Compute_H(displacements)

Returns: the L matrix

◆ Compute_Pt()

static void XC::EICR::Compute_Pt	(	size_t	num_nodes,
		MatrixType &	P
	)

inlinestatic

Computes the Translational Projector Matrix.

The output is a square matrix of size num_nodes*6. Note that 6 Degrees Of Freedom are assumed for each node.

Parameters

num_nodes	the number of nodes
P	the Translational Projector Matrix

◆ Compute_S()

static void XC::EICR::Compute_S	(	const NodeContainerType &	nodes,
		MatrixType &	S
	)

inlinestatic

Computes the Spin Lever Matrix.

The output is a rectangular matrix of 3 columns and nodes.size()*6 rows. Note that 6 Degrees Of Freedom are assumed for each node.

Parameters

nodes	the input nodes
S	the Spin Lever Matrix

◆ GetBlock() [1/2]

static void XC::EICR::GetBlock	(	const VectorType &	A,
		size_t	begin,
		size_t	end,
		VectorType &	B
	)

inlinestatic

Copies the block [begin:end[ from A to B.

B size must be end-begin. Note: no size check is made!

Parameters

A	the first vector
begin	the first index
end	the last+1 index
B	the second vector

◆ GetBlock() [2/2]

static void XC::EICR::GetBlock	(	const MatrixType &	A,
		size_t	begin,
		size_t	end,
		MatrixType &	B
	)

inlinestatic

Copies the block [begin:end[ from A to B.

B size must be end-begin. Note: no size check is made!

Parameters

A	the first matrix
begin	the first index
end	the last+1 index
B	the second matrix

◆ OuterProd()

void XC::EICR::OuterProd	(	const VectorType &	A,
		const VectorType &	B,
		MatrixType &	C
	)

static

computes the outer product A x B, in C.

Note: no size check is made!

Parameters

A	the first vector
B	the second vector
C	the output matrix

◆ SetBlock()

static void XC::EICR::SetBlock	(	MatrixType &	A,
		size_t	begin,
		size_t	end,
		const MatrixType &	B
	)

inlinestatic

Copies the block [begin:end[ from B to A.

B size must be end-begin. Note: no size check is made!

Parameters

A	the first vector
begin	the first index
end	the last+1 index
B	the second vector

◆ SetIdentity()

static void XC::EICR::SetIdentity	(	size_t	n,
		MatrixType &	I,
		double	value = `1.0`
	)

inlinestatic

Sets the input matrix to the identity of requested size.

Resize is done if necessary

Parameters

n	the number of rows and columns
I	the input/output matrix
value	(optional, default = 1) the value on the diagonal terms

◆ SetZero()

void XC::EICR::SetZero	(	size_t	n,
		size_t	m,
		MatrixType &	I
	)

static

Sets the input matrix to the zero matrix of requested size.

Resize is done if necessary

Parameters

n	the number of rows
n	the number of columns
I	the input/output matrix

◆ Spin() [1/2]

template<class TVec , class TMat >

static void XC::EICR::Spin	(	const TVec &	V,
		TMat &	S
	)

inlinestatic

Computes the Spin of the input vector V, and saves the result into the output matrix S.

Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)

◆ Spin() [2/2]

template<class TVec , class TMat >

static void XC::EICR::Spin	(	const TVec &	V,
		TMat &	S,
		double	mult
	)

inlinestatic

Computes the Spin of the input vector V, and saves the result into the output matrix S.

This version uses a multiplier for the output values. Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)
mult	the multiplier for the output values

◆ Spin_AtRow() [1/4]

template<class TVec , class TMat >

static void XC::EICR::Spin_AtRow	(	const TVec &	V,
		TMat &	S,
		size_t	row_index
	)

inlinestatic

Computes the Spin of the input vector V, and saves the result into the output matrix S, at the specified row index.

Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)
row_index	the index of the first row in the output matrix where the spin has to be saved

◆ Spin_AtRow() [2/4]

template<class TVec , class TMat >

static void XC::EICR::Spin_AtRow	(	const TVec &	V,
		TMat &	S,
		size_t	vector_index,
		size_t	matrix_row_index
	)

inlinestatic

Computes the Spin of the input vector V, from the specified index, and saves the result into the output matrix S, at the specified row index.

Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)
vector_index	the index of the first component of the input vector to be used to compute the spin
row_index	the index of the first row in the output matrix where the spin has to be saved

◆ Spin_AtRow() [3/4]

template<class TVec , class TMat >

static void XC::EICR::Spin_AtRow	(	const TVec &	V,
		TMat &	S,
		double	mult,
		size_t	row_index
	)

inlinestatic

Computes the Spin of the input vector V, and saves the result into the output matrix S, at the specified row index.

This version uses a multiplier for the output values. Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)
mult	the multiplier for the output values
row_index	the index of the first row in the output matrix where the spin has to be saved

◆ Spin_AtRow() [4/4]

template<class TVec , class TMat >

static void XC::EICR::Spin_AtRow	(	const TVec &	V,
		TMat &	S,
		double	mult,
		size_t	vector_index,
		size_t	matrix_row_index
	)

inlinestatic

Computes the Spin of the input vector V, from the specified index, and saves the result into the output matrix S, at the specified row index.

This version uses a multiplier for the output values. Note: no check is made on the size of the input-output arguments.

Parameters

V	the input vector (assumed size: >= 3)
S	the output matrix (assumed size: >= 3x3)
mult	the multiplier for the output values
vector_index	the index of the first component of the input vector to be used to compute the spin
row_index	the index of the first row in the output matrix where the spin has to be saved

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

src/domain/mesh/element/utils/coordTransformation/ASDEICR.h
src/domain/mesh/element/utils/coordTransformation/ASDEICR.cc

Public Types

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ Compute_H()

◆ Compute_L()

◆ Compute_Pt()

◆ Compute_S()

◆ GetBlock() [1/2]

◆ GetBlock() [2/2]

◆ OuterProd()

◆ SetBlock()

◆ SetIdentity()

◆ SetZero()

◆ Spin() [1/2]

◆ Spin() [2/2]

◆ Spin_AtRow() [1/4]

◆ Spin_AtRow() [2/4]

◆ Spin_AtRow() [3/4]

◆ Spin_AtRow() [4/4]