rbe_solve

compas_cra.equilibrium.rbe_solve(assembly, mu=0.84, density=1.0, verbose=False, timer=False)[source]

RBE solver with penalty formulation using Pyomo + IPOPT.

Parameters

  • assembly (Assembly) – The rigid block assembly.

  • mu (float, optional) – Friction coefficient value.

  • density (float, optional) – Density of the block material.

  • verbose (bool, optional) – Print information during the execution of the algorithm.

  • timer (bool, optional) – Time the solving time.

Returns

Assembly – The assembly is updated in place, also return Assembly for compas.rpc and compas.cloud

Notes

This function solves the following optimisation problem, Eq.(6) :

\[\begin{split}\begin{align} \begin{split} \min_{\bf{\tilde{f}}} \quad & \frac{1}{2}\:{\bf{\tilde{f}}^\intercal}\:{\bf{H}}\:{\bf{\tilde{f}}} \\ \textrm{s.t.} \quad & {{\bf{A}}_{eq}}\:{\bf{B}}\:{\bf{\tilde{f}}} = -{\bf{p}} \\ & {\bf{A}}_{fr}\:{\bf{B}}\:{\bf{\tilde{f}}} \le {\bf{0}} \\ & f_{jkn}^{i+}\, ,f_{jkn}^{i-} \ge 0 \;, \quad \forall i,j,k \;, \end{split} \end{align}\end{split}\]

For more information please check our research paper: Coupled Rigid-Block Analysis: Stability-Aware Design of Complex Discrete-Element Assemblies