Shape optimization of free-form shell structures combining static and dynamic behaviors

Abstract

Structural performance under seismic loads is necessarily checked after the static load is considered in the design of a structure. If it fails to pass the specified safety requirements, the structure has to be redesigned, resulting in additional time and computational cost. Therefore, in this study, we present four shape optimization problems to obtain rational shapes for free-form shell structures with both high static and dynamic performances. The strain energy under static loads is the measure of static performance, and the lower bound on the fundamental natural frequency or strain energy under seismic loads is the measure of dynamic performance. An optimization problem is first formulated for minimizing the strain energy under frequency constraint, where the self-weight and live loads are applied. The strain energy corresponding to the equivalent seismic static load is next minimized. To prevent unfavorable shape when the design variables are dense, we also consider the surface curvature as the other objective function in a bi-objective optimization problem. Several numerical examples are given to demonstrate the effectiveness of the proposed method.