Simulated annealing applied to the optimal plastic design of circular steel plates

This article describes an application of the simulated annealing (SA) algorithm to a structural problem, consisting in finding a minimum-weight circular plate of the imposed limit load. For technological reasons, the considered plates are divided into rings of constant thickness. The boundaries of these rings may vary, so the thickness and size of each ring are the design variables to be considered. Although SA is mostly applied to handle combinatorial optimization problems, the present study shows that it can also be efficient in the field of mechanical engineering. Some particular aspects of the study are thoroughly described. For instance, technological constraints have to be considered: lower and upper bounds are imposed on the thickness of each ring, and a lower bound is imposed on the ring width. These constraints are not taken into account by means of a classical penalty method, but by a set of dedicated procedures. The particular constraint of the imposed limit load is treated by solving the inverse problem at each iteration: the limit load of the current solution is computed and the geometry of the plate is adapted to fit the assigned value. After discussion about points of attention, general conclusions are drawn from the performances of SA in its present implementation. The obtained results show that the algorithm exhibits satisfactory levels of reliability and efficiency. Copyright q 2007 John Wiley & Sons, Ltd