Free-form optimization of a shell structure for minimizing maximum stress

Abstract

In this paper, we present a parameter-free free-form optimization method for the strength design problem of a shell structure. The maximum von Mises stress is minimized under a given volume constraint condition. The optimum design problem is formulated under the assumptions that a shell is varied in the out-of-plane direction to the surface and the thickness is constant. The issue of non-differentiability inherent in this min-max problem is avoided by transforming the singular local measure to a smooth differentiable integral functional by using the Kreisselmeier-Steinhauser function. The shape gradient function and optimality conditions theoretically derived are applied to the free-form optimization method for shells. With this method, the smooth optimal free-form of a shell structure is determined without any shape design parameterization, while minimizing the objective functional. Design examples are presented to demonstrate the validity of this free-form optimization method for minimizing the maximum stress of a shell structure.