Free-form optimization of a frame structure for strength maximization

Abstract

In this paper, we present a parameter-free free-form optimization method for the strength design problem of a frame structure. The maximum von Mises stress is minimized under a given volume constraint. The strength design problems are formulated as distributed-parameter optimization problems under the assumptions that each member is varied in the off-axis direction to the centroidal-axis and the cross section is not varied with respect to the iteration process. 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 functions and optimality conditions theoretically derived are applied to the free-form optimization method for frames. With this method, the smooth optimal free-form of a frame 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 strength design problems of a frame structure.

Keywords

• shape optimization
• frame structure
• free-form optimization
• von mises stress
• strength design
• kreisselmeier-steinhauser function
• min-max problem