get_aitkendisp module

Modules for calculating aitkens displacement.

Revision: 1.0.0 $Date: 24/01/2023 16:26$

History

  1. 1.0.0 - Initial Module Creation

Todo

This function should be generalized for any physical values.

get_aitkendisp.main()[source]

main sequence

\begin{gather}\label{eq:displacement_relax} \pmb{u}^{k+1}_\mathrm{s} = \omega^{k+1} \tilde{\pmb{u}}^{k+1}_\mathrm{s} + (1 - \omega^{k+1}) \pmb{u}^{k}_\mathrm{s}, \end{gather}
\begin{gather}\label{eq:aitken_relaxation} \omega^{k+1} = \omega^{k} \left( 1 - \dfrac{(\Delta \tilde{\pmb{u}}^{k+1}_\mathrm{s} - \Delta \tilde{\pmb{u}}^{k}_\mathrm{s})^T \Delta \tilde{\pmb{u}}^{k}_\mathrm{s}} {(\Delta \tilde{\pmb{u}}^{k+1}_\mathrm{s} - \Delta \tilde{\pmb{u}}^{k}_\mathrm{s})^T (\Delta \tilde{\pmb{u}}^{k+1}_\mathrm{s} - \Delta \tilde{\pmb{u}}^{k}_\mathrm{s})} \right). \end{gather}

where,

\begin{gather}\label{eq:delta_u} \Delta \tilde{\pmb{u}}^{k+1}_\mathrm{s} = \tilde{\pmb{u}}^{k+1}_\mathrm{s} - \pmb{u}^{k}_\mathrm{s}, \end{gather}
Procedure:

  1. read displacement of previous and currenct step. \(\pmb{u}^{k}_\mathrm{s},~\tilde{\pmb{u}}^{k+1}_\mathrm{s}\)

  2. read increment of displacement from preprevious step to previsous step. \(\Delta \tilde{\pmb{u}}^{k}_\mathrm{s}\)

  3. read relaxation parameter in previous step. \(\omega^{k}\)

  4. calculate increment of displacement from previous step to current step. \(\Delta \tilde{\pmb{u}}^{k+1}_\mathrm{s}\)

  5. update relaxation parameter. \(\omega^{k+1}\)

  6. update displacement. \(\pmb{u}^{k+1}_\mathrm{s}\)

Input files:

  • ‘dispStruct_fem.dat’: displacement from FEM in the current step.

  • ‘dispStruct_pre.dat’: displacement in the previous step after relaxation.

  • ‘dispStructInc_pre.dat’: increment of displacement from preprevious step to previous step.

  • ‘theta_pre.dat’: relaxation parameter in the previsous step.

Output files:

  • ‘dispStructInc.dat’: increment of displacement from previous step to current step.

  • ‘theta.dat’: relaxation parameter in the current step.

  • ‘dispStruct.dat’: displacement after relaxatino in the current step.

Parameters

None –

Returns

None

Documentation last updated: Jan. 24, 2023 - Shugo Date