Topological optimization of truss structures using simulated annealing

A design procedure for integrating topological decision making in the framework of structural optimization is presented. The proposed approach facilitates (i) generation and evaluation of alternate structural topologies, and (ii) development of detailed designs for promising concepts. In contrast with the ground-structure approach, the proposed method allows for an introduction of new members in an existing topology. This is done using 0-1 variables to represent topological decisions involving a choice between alternative designs. Since the topological variables are discrete in nature and the member cross-sections are assumed to be continuous, the topological optimization problem has mixed discrete-continuous variables. This problem is solved using a simulated annealing approach wherein the search for an optimum topology is simulated as a relaxation of the stochastic structural system. A probabilistic acceptance criterion is used to accept/reject candidate designs. Numerical results obtained using simulated annealing for single and multiobjective topological optimization of truss structures are presented. For multiobjective problems, a cooperative game theoretic approach is used to model the multiple objective functions in the problem formulation.