Class GooseFEM::Tyings::Periodic#
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class Periodic#
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.
Public Functions
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template<class C, class D, class S, class T>
inline Periodic(const C &coor, const D &dofs, const S &control_dofs, const T &nodal_tyings)# Constructor.
- Template Parameters
- 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].
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template<class C, class D, class S, class T, class U>
inline Periodic(const C &coor, const D &dofs, const S &control_dofs, const T &nodal_tyings, const U &iip)# Constructor.
- Template Parameters
- 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.
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inline size_t nnd() const#
- Returns
Number of dependent DOFs.
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inline size_t nni() const#
- Returns
Number of independent DOFs.
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inline size_t nnu() const#
- Returns
Number of independent unknown DOFs.
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inline size_t nnp() const#
- Returns
Number of independent prescribed DOFs.
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inline const array_type::tensor<size_t, 2> &dofs() const#
- Returns
DOF-numbers per node, as used internally (after renumbering), [nnode, ndim].
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inline const array_type::tensor<size_t, 2> &control() const#
- Returns
DOF-numbers for each control node, as used internally (after renumbering), [ndim, ndim].
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inline const array_type::tensor<size_t, 2> &nodal_tyings() const#
Return the applied nodal tyings.
Per tying (row) two node numbers are specified, according to the convention (independent, dependent).
- Returns
[ntyings, 2].
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inline array_type::tensor<size_t, 1> iid() const#
Dependent DOFs.
- Returns
List of DOF numbers.
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inline array_type::tensor<size_t, 1> iii() const#
Independent DOFs.
- Returns
List of DOF numbers.
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inline array_type::tensor<size_t, 1> iiu() const#
Independent unknown DOFs.
- Returns
List of DOF numbers.
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inline array_type::tensor<size_t, 1> iip() const#
Independent prescribed DOFs.
- Returns
List of DOF numbers.
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inline 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.
\( u_d = C_{di} u_i \)
Note that this can be further partitioned in
\( u_d = C_{du} u_u + C_{dp} u_p \)
- Returns
Sparse matrix.