Shape optimization of 2D structures using simulated annealing

The goal of this study is to obtain globally optimum shapes for two-dimensional structures subject to quasi-static loads and restraints. For this purpose a technique is proposed, using which the volume (or weight) of a structure can be minimized. The emphasis is on how one can define the shape precisely, and find a shape that accurately reflects the globally optimum shape.As design constraints, stresses developed in the structure should not exceed the maximum allowable stress, and connectivity of the structure should not be lost during shape changes. Optimization is achieved by a stochastic search algorithm called direct simulated annealing (DSA), which seeks the global minimum through randomly generated configurations. In order to obtain random configurations, a boundary variation technique is used. In this technique, a set of key points is chosen and connected by cubic splines to describe the boundary of the structure. Whenever the positions of the key points are changed in random directions, a new shape is obtained. Thus, coordinates of the key points serve as design variables. In order to apply the optimization procedure, a general computer code was developed using ANSYS Parametric Design Language. A number of cases were examined to test its effectiveness. The results show that this technique can be applied to two-dimensional shape optimization problems with high reliability even for cases where the entire free boundary is allowed to vary.