Nodal tyings per periodic boundary conditions. More...

#include <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. More...

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. More...

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. More...

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

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

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

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

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. More...

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

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

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 237 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 307 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 270 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 166 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 157 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 188 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 198 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 218 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 208 of file TyingsPeriodic.h.

◆ nnd()

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

inline

Returns: Number of dependent DOFs.

Definition at line 125 of file TyingsPeriodic.h.

◆ nni()

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

inline

Returns: Number of independent DOFs.

Definition at line 133 of file TyingsPeriodic.h.

◆ nnp()

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

inline

Returns: Number of independent prescribed DOFs.

Definition at line 149 of file TyingsPeriodic.h.

◆ nnu()

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

inline

Returns: Number of independent unknown DOFs.

Definition at line 141 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 178 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()