Open Access

ARTICLE

Multigrid Implementation of Cellular Automata for Topology Optimization of Continuum Structures

R. Zakhama^1,2,3, M.M. Abdalla², H. Smaoui^1,3, Z. Gürdal²

1 Civil Engineering, National School of Engineering at Tunis, Tunis, Tunisia.
2 Aerospace Structures, Technical University of Delft, Delft, The Netherlands.
3 LASMAP, Polytechnic School of Tunisia, La Marsa, Tunisia.

Computer Modeling in Engineering & Sciences 2009, 51(1), 1-26. https://doi.org/10.3970/cmes.2009.051.001

Abstract

A multigrid accelerated cellular automata algorithm for two and three dimensional continuum topology optimization problems is presented. The topology optimization problem is regularized using the traditional SIMP approach. The analysis rules are derived from the principle of minimum total potential energy, and the design rules are derived based on continuous optimality criteria interpreted as local Kuhn-Tucker conditions. Three versions of the algorithm are implemented; a cellular automata based design algorithm, a baseline multigrid algorithm for analysis acceleration and a full multigrid integrated analysis and design algorithm. It is shown that the multigrid accelerated cellular automata scheme is a powerful tool to solve topology optimization problems. This is demonstrated quantitatively by comparing the convergence time of the multigrid algorithm for different discretization levels, with that of the same design algorithm where the analysis is performed by a commercial finite element code.

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