Multi material topology optimization with hybrid cellular automata

Abstract

Topology Optimization is a technique that allows for the obtaining structures which maximize the use of the material. This is done by intelligently deciding the binary distribution of solid material and void, in a discretized given space. Several researchers have provided methods to tackle binary topology optimization. New ef- forts are focused on extending the application for multi-phase optimizations. At the industrial level, several components designed are made up of more than one material to reduce weight and production costs. The objective of this work is to implement the algorithm of Hybrid Cellular Automaton for multi-material topology optimiza- tion. The commonly used interpolation rule SIMP, which allows to relate the design variables to the mechanical properties of the material, is replaced by ordered SIMP interpolation function. The multiple volume constraints are applied sequentially, starting with the most elastic material. When a constraint is satisfied, the elements assigned to this material remain passive by a defined number of iterations to promote the convergence of the solution. Examples are shown for static and dynamic loads. The work demonstrates the versatility of algorithms based on control systems to solve problems of multiple phases and transient response fields.