A New Solving Method of the Compliance Topology Optimization Problem of Continuum Structures under Multiple Load Cases

Abstract

Abstract：Most of engineering structures work under multiple load cases, and topology compliance minimization under multiple load cases are of important engineering value. A new compliance topology optimization method of continuum structures under multiple load cases with a volume constraint is proposed. Firstly, being referred to the bound formulation method, original multiple objective functions dealing with structural compliance under multiple load cases are transferred to multiple constraints by using a bound variable, and a novel quadratic function of the bound variable is treated as a new objective function. At the same time, being integrated with a varied volume limit scheme, a novel and equivalent approximate topology model is constructed. Then, convex and separable quadratic approximate functions for the volume and structural compliance under multiple load cases, are formed, based on the rational approximation for material properties (RAMP) and the method of moving asymptotes (MMA). The approximate optimization model is solved by adopting a smooth dual algorithm, and a new compliance topology optimization procedure, possessing convergence, is proposed. It is concluded from given examples that the proposed method is higher efficient for generating a same optimal topology, or may obtain a more optimal topology than the existed methods; and an optimal topology with clear 0/1 distribution, may robustly be obtained by the proposed method. Key words：structural topology optimization；multiple load cases；structural compliance；dual algorithm；multiple objective optimization * 国家自然科学基金(11372055, 11772070)和工程车辆轻量化与可靠性技 术湖南省高校重点实验室(长沙理工大学)开放基金(2013KFJJ03)资助项 目。20170612 收到初稿，20170919 收到修改稿