Design optimization of moment frame structures by the method of inscribed hyperspheres

Abstract

In this study, the method of inscribed hyperspheres (IHS) is presented and applied for the optimal design of 2-D steel moment frame structures. The weight of the structures, which is a function of the design variables (cross-sectional areas), is optimized subject to stress, displacement, size limits, and the variables’ linkage constraints. The IHS approach is employed to find the acceptable centers. The basic idea of this method is to inscribe the largest possible sphere in a closed space that has been created by the objective function and linearized constraints in each step. The obtained results were presented in discrete and continuous variables and compared to the results reported in the literature. This comparison showed the efficiency of this method. Also, a new mixed method of combining the optimality criteria (OC) method and the IHS method is presented in this study. It was observed that the number of iterations needed to reach the optimal solution using this new method is less than that of the above two methods when used individually, and the problem is converged to the optimal answer with extremely low iterations.