Description

Collaboration diagram for Mathematical support:

Namespaces

 chrono::fea::ChRotUtils
 Utility functions for rotations in 3D and their derivatives.
 

Classes

class  chrono::fea::ChGaussIntegrationRule
 Class for the management of the Gauss Quadrature in 1D, 2D or 3D space. More...
 
class  chrono::fea::ChGaussPoint
 Class for a Gauss point, that has a position (1D-3D) and a weight. More...
 
class  chrono::fea::ChMatrixCorotation< Real >
 Perform a corotation (warping) of a K matrix by pre- or post- multiplying it with a C matrix that has 3x3 rotation matrices R as diagonal blocks, so that C*K means: More...
 
class  chrono::fea::PolarDecomposition
 Polar decomposition of a general 3x3 matrix. More...
 
class  chrono::fea::ChPolarDecomposition< Real >
 Perform a polar decomposition of a 3x3 P matrix in order to retrieve the orthogonal Q and the symmetric S form, as P=Q*S. More...
 

Functions

template<int N>
bool chrono::fea::LU_factor (ChMatrixNM< double, N, N > &A, ChMatrixNM< int, N, 1 > &INDX, bool &pivoting)
 In-place LU factorization. More...
 
template<int N>
void chrono::fea::LU_solve (const ChMatrixNM< double, N, N > &A, const ChMatrixNM< int, N, 1 > &INDX, ChMatrixNM< double, N, 1 > &B)
 LU linear system solution (back substitution) More...
 
static void chrono::fea::ChMatrixCorotation< Real >::ComputeCK (const ChMatrix< Real > &K, const ChMatrix33< Real > &R, const int nblocks, ChMatrix< Real > &CK)
 Perform a corotation (warping) of a K matrix by pre-multiplying it with a C matrix; C has 3x3 rotation matrices R as diagonal blocks. More...
 
static void chrono::fea::ChMatrixCorotation< Real >::ComputeKCt (const ChMatrix< Real > &K, const ChMatrix33< Real > &R, const int nblocks, ChMatrix< Real > &KC)
 Perform a corotation (warping) of a K matrix by post-multiplying it with a transposed C matrix; C has 3x3 rotation matrices R as diagonal blocks. More...
 
static void chrono::fea::ChMatrixCorotation< Real >::ComputeCK (const ChMatrix< Real > &K, const std::vector< ChMatrix33< Real > * > &R, const int nblocks, ChMatrix< Real > &CK)
 Perform a corotation (warping) of a K matrix by pre-multiplying it with a C matrix; C has 3x3 rotation matrices R as diagonal blocks (generic version with different rotations) More...
 
static void chrono::fea::ChMatrixCorotation< Real >::ComputeKCt (const ChMatrix< Real > &K, const std::vector< ChMatrix33< Real > * > &R, const int nblocks, ChMatrix< Real > &KC)
 Perform a corotation (warping) of a K matrix by post-multiplying it with a transposed C matrix; C has 3x3 rotation matrices R as diagonal blocks (generic version with different rotations) More...
 

Function Documentation

template<class Real >
void chrono::fea::ChMatrixCorotation< Real >::ComputeCK ( const ChMatrix< Real > &  K,
const ChMatrix33< Real > &  R,
const int  nblocks,
ChMatrix< Real > &  CK 
)
static

Perform a corotation (warping) of a K matrix by pre-multiplying it with a C matrix; C has 3x3 rotation matrices R as diagonal blocks.

Parameters
Kmatrix to pre-corotate
R3x3 rotation matrix
nblocksnumber of rotation blocks
CKresult matrix: C*K
template<class Real >
void chrono::fea::ChMatrixCorotation< Real >::ComputeCK ( const ChMatrix< Real > &  K,
const std::vector< ChMatrix33< Real > * > &  R,
const int  nblocks,
ChMatrix< Real > &  CK 
)
static

Perform a corotation (warping) of a K matrix by pre-multiplying it with a C matrix; C has 3x3 rotation matrices R as diagonal blocks (generic version with different rotations)

generic version

Parameters
Kmatrix to pre-corotate
R3x3 rotation matrices
nblocksnumber of rotation blocks
CKresult matrix: C*K
template<class Real >
void chrono::fea::ChMatrixCorotation< Real >::ComputeKCt ( const ChMatrix< Real > &  K,
const ChMatrix33< Real > &  R,
const int  nblocks,
ChMatrix< Real > &  KC 
)
static

Perform a corotation (warping) of a K matrix by post-multiplying it with a transposed C matrix; C has 3x3 rotation matrices R as diagonal blocks.

Parameters
Kmatrix to post-corotate
R3x3 rotation matrix (will be used transposed)
nblocksnumber of rotation blocks
KCresult matrix: C*K
template<class Real >
void chrono::fea::ChMatrixCorotation< Real >::ComputeKCt ( const ChMatrix< Real > &  K,
const std::vector< ChMatrix33< Real > * > &  R,
const int  nblocks,
ChMatrix< Real > &  KC 
)
static

Perform a corotation (warping) of a K matrix by post-multiplying it with a transposed C matrix; C has 3x3 rotation matrices R as diagonal blocks (generic version with different rotations)

generic version

Parameters
Kmatrix to post-corotate
R3x3 rotation matrices (used transposed)
nblocksnumber of rotation blocks
KCresult matrix: C*K
template<int N>
bool chrono::fea::LU_factor ( ChMatrixNM< double, N, N > &  A,
ChMatrixNM< int, N, 1 > &  INDX,
bool &  pivoting 
)

In-place LU factorization.

Return false if the matrix is (close to) singular

Parameters
[in,out]Amatrix to be factorized
[out]INDXvector of pivots
[out]pivotingtrue if pivoting was required; false otherwise
template<int N>
void chrono::fea::LU_solve ( const ChMatrixNM< double, N, N > &  A,
const ChMatrixNM< int, N, 1 > &  INDX,
ChMatrixNM< double, N, 1 > &  B 
)

LU linear system solution (back substitution)

Parameters
[in]ALU factorized matrix
[out]INDXvector of pivots
[in,out]Bon entry, the RHS; on return, the solution vector