A Multi-objective Structural Optimization Using Optimality Criteria and Cellular Automata

This paper is devoted to the simultaneous weight and stiffness optimization of two dimensional structures. The necessary optimality conditions are derived and the obtained optimality criterion is briefly explained. Based on the paradigm of cellular automata, a local rule is constructed which alleviates the well known problems of mesh dependency and checker-boarding in topological structural optimization. It is shown that implementation of this algorithm is useful in prevention of the formation of undesirable members in the resulting layouts. In this approach, contrary to the conventional topological structural optimization methods, the shape and boundaries of the two dimensional continuum are not fixed and can undergo considerable changes during the optimization process. Hence, This approach may be considered as a generalized structural optimization method. To demonstrate the advantages of the method a couple of examples are presented.