Optimum topology reinforcement design of disk ad plate structures with multiple stiffness and eigenfrequency objectives

摘要

This paper deals with topology optimization of statically loaded or freely vibrating disk and plate structures, and with layout optimization of different types of integral rib-reinforcement of plates. The design parametrization is based on different configurations of layered microstructures, and the effective stiffness properties of the microstructures are derived in a unified way by a homogenization approach. The effects of using microstructures of second rank and of arbitrary rank (based on moment variables) are studied and compared using examples. All structures are analyzed applying anisotropic Mindlin finite elements with membrance capability. For the disk and plate structures under consideration, special emphasis is devoted to problems of stiffness optimization subject to several load cases and problems of optimization of eigenfrequencies of free vibration that belong to a given spectrum of eigenfrequencies, i.e. optimization problems that imply multiobjective formulations are considered. The multiobjective problems are treated via a max-min formulation based on a variable lower bound technique, and this approach is shown to yield much more significant results than the usual weighted sum formulation of multiobjective problems. Several illustrative numerical examples of multiobjective topology and layout optimization problems of statically loaded and vibrating disks and plates are presented in the paper.