Nodal tyings per periodic boundary conditions. More...

#include <GooseFEM/TyingsPeriodic.h>

Public Member Functions
template<class C , class D , class S , class T >
	Periodic (const C &coor, const D &dofs, const S &control_dofs, const T &nodal_tyings)
	Constructor.

template<class C , class D , class S , class T , class U >
	Periodic (const C &coor, const D &dofs, const S &control_dofs, const T &nodal_tyings, const U &iip)
	Constructor.

size_t	nnd () const

size_t	nni () const

size_t	nnu () const

size_t	nnp () const

const array_type::tensor< size_t, 2 > &	dofs () const

const array_type::tensor< size_t, 2 > &	control () const

const array_type::tensor< size_t, 2 > &	nodal_tyings () const
	Return the applied nodal tyings.

array_type::tensor< size_t, 1 >	iid () const
	Dependent DOFs.

array_type::tensor< size_t, 1 >	iii () const
	Independent DOFs.

array_type::tensor< size_t, 1 >	iiu () const
	Independent unknown DOFs.

array_type::tensor< size_t, 1 >	iip () const
	Independent prescribed DOFs.

Eigen::SparseMatrix< double >	Cdi () const
	Return tying matrix such as to get the dependent DOFs \( u_d \) from the independent DOFs \( u_i \) as follows.

Eigen::SparseMatrix< double >	Cdu () const
	Unknown part of the partitioned tying matrix, see Cdi().

Eigen::SparseMatrix< double >	Cdp () const
	Prescribed part of the partitioned tying matrix, see Cdi().

Detailed Description

Nodal tyings per periodic boundary conditions.

The idea is that the displacement of all DOFs of a node are tied to another node and to the average displacement gradient. The latter is applied/measured using 'virtual' control nodes.

Consider the DOF list \( u \) renumbered such that it is split up in independent and dependent DOFs as follows

\( u = \begin{bmatrix} u_i \\ u_d \end{bmatrix}\)

whereby the independent DOFs are furthermore split up in unknown and prescribed nodes as follows

\( u_i = \begin{bmatrix} u_u \\ u_p \end{bmatrix}\)

such that

\( u = \begin{bmatrix} u_u \\ u_p \\ u_d \end{bmatrix}\)

Todo: Document how the DOFs are tied to the control nodes, and what the has to do with the mean.

Definition at line 46 of file TyingsPeriodic.h.

Constructor & Destructor Documentation

◆ Periodic() [1/2]

template<class C , class D , class S , class T >

GooseFEM::Tyings::Periodic::Periodic	(	const C &	coor,
		const D &	dofs,
		const S &	control_dofs,
		const T &	nodal_tyings )

inline

Constructor.

Template Parameters

C	array_type::tensor<double, 2>
D	array_type::tensor<size_t, 2>
S	array_type::tensor<size_t, 2>
T	array_type::tensor<size_t, 2>

Parameters

coor	Nodal coordinates [nnode, ndim].
dofs	DOF-numbers per node [nnode, ndim].
control_dofs	DOF-numbers per control node [ndim, ndim].
nodal_tyings	List of nodal tyings, see nodal_tyings(). [ntyings, 2].

Definition at line 63 of file TyingsPeriodic.h.

◆ Periodic() [2/2]

template<class C , class D , class S , class T , class U >

GooseFEM::Tyings::Periodic::Periodic	(	const C &	coor,
		const D &	dofs,
		const S &	control_dofs,
		const T &	nodal_tyings,
		const U &	iip )

inline

Constructor.

Template Parameters

C	array_type::tensor<double, 2>
D	array_type::tensor<size_t, 2>
S	array_type::tensor<size_t, 2>
T	array_type::tensor<size_t, 2>
U	array_type::tensor<size_t, 1>

Parameters

coor	Nodal coordinates [nnode, ndim].
dofs	DOF-numbers per node [nnode, ndim].
control_dofs	DOF-numbers per control node [ndim, ndim].
nodal_tyings	List of nodal tyings, see nodal_tyings(). [ntyings, 2].
iip	List of prescribed DOF-numbers.

Definition at line 83 of file TyingsPeriodic.h.

Member Function Documentation

◆ Cdi()

Eigen::SparseMatrix< double > GooseFEM::Tyings::Periodic::Cdi ( ) const

inline

Return tying matrix such as to get the dependent DOFs \( u_d \) from the independent DOFs \( u_i \) as follows.

\( u_d = C_{di} u_i \)

Note that this can be further partitioned in

\( u_d = C_{du} u_u + C_{dp} u_p \)

See Cdu() and Cdp().

Returns: Sparse matrix.

Definition at line 238 of file TyingsPeriodic.h.

◆ Cdp()

Eigen::SparseMatrix< double > GooseFEM::Tyings::Periodic::Cdp ( ) const

inline

Prescribed part of the partitioned tying matrix, see Cdi().

Returns: Sparse matrix.

Definition at line 310 of file TyingsPeriodic.h.

◆ Cdu()

Eigen::SparseMatrix< double > GooseFEM::Tyings::Periodic::Cdu ( ) const

inline

Unknown part of the partitioned tying matrix, see Cdi().

Returns: Sparse matrix.

Definition at line 272 of file TyingsPeriodic.h.

◆ control()

const array_type::tensor< size_t, 2 > & GooseFEM::Tyings::Periodic::control ( ) const

inline

Returns: DOF-numbers for each control node, as used internally (after renumbering), [ndim, ndim].

Definition at line 167 of file TyingsPeriodic.h.

◆ dofs()

const array_type::tensor< size_t, 2 > & GooseFEM::Tyings::Periodic::dofs ( ) const

inline

Returns: DOF-numbers per node, as used internally (after renumbering), [nnode, ndim].

Definition at line 158 of file TyingsPeriodic.h.

◆ iid()

array_type::tensor< size_t, 1 > GooseFEM::Tyings::Periodic::iid ( ) const

inline

Dependent DOFs.

Returns: List of DOF numbers.

Definition at line 189 of file TyingsPeriodic.h.

◆ iii()

array_type::tensor< size_t, 1 > GooseFEM::Tyings::Periodic::iii ( ) const

inline

Independent DOFs.

Returns: List of DOF numbers.

Definition at line 199 of file TyingsPeriodic.h.

◆ iip()

array_type::tensor< size_t, 1 > GooseFEM::Tyings::Periodic::iip ( ) const

inline

Independent prescribed DOFs.

Returns: List of DOF numbers.

Definition at line 219 of file TyingsPeriodic.h.

◆ iiu()

array_type::tensor< size_t, 1 > GooseFEM::Tyings::Periodic::iiu ( ) const

inline

Independent unknown DOFs.

Returns: List of DOF numbers.

Definition at line 209 of file TyingsPeriodic.h.

◆ nnd()

size_t GooseFEM::Tyings::Periodic::nnd ( ) const

inline

Returns: Number of dependent DOFs.

Definition at line 126 of file TyingsPeriodic.h.

◆ nni()

size_t GooseFEM::Tyings::Periodic::nni ( ) const

inline

Returns: Number of independent DOFs.

Definition at line 134 of file TyingsPeriodic.h.

◆ nnp()

size_t GooseFEM::Tyings::Periodic::nnp ( ) const

inline

Returns: Number of independent prescribed DOFs.

Definition at line 150 of file TyingsPeriodic.h.

◆ nnu()

size_t GooseFEM::Tyings::Periodic::nnu ( ) const

inline

Returns: Number of independent unknown DOFs.

Definition at line 142 of file TyingsPeriodic.h.

◆ nodal_tyings()

const array_type::tensor< size_t, 2 > & GooseFEM::Tyings::Periodic::nodal_tyings ( ) const

inline

Return the applied nodal tyings.

Per tying (row) two node numbers are specified, according to the convention (independent, dependent).

Returns: [ntyings, 2].

Definition at line 179 of file TyingsPeriodic.h.

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

GooseFEM/TyingsPeriodic.h

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Periodic() [1/2]

◆ Periodic() [2/2]

Member Function Documentation

◆ Cdi()

◆ Cdp()

◆ Cdu()

◆ control()

◆ dofs()

◆ iid()

◆ iii()

◆ iip()

◆ iiu()

◆ nnd()

◆ nni()

◆ nnp()

◆ nnu()

◆ nodal_tyings()