Topology optimization of structures under multiple loading cases with a new compliance–volume product

Abstract

This article proposes a new topology optimization method for the design of structures under multiple loading cases. The design is formulated as a multi-objective optimization problem by minimizing a new compliance–volume product, which optimizes the overall stiffness and volume simultaneously to avoid the empirical decision on design constraints and obtain an even lower structural volume. A normalized exponential weighted criterion (NEWC) method is included in the multi-objective optimization problem for the capture of the entire Pareto frontier. A weight evaluation method, in terms of the fuzzy multiple-attribute group decision-making (FMAGDM) theory, is incorporated in the problem to evaluate the weights of the objectives and guarantee the optimal design in an acceptable level. The solid isotropic material with penalty (SIMP) method is used to represent the dependence of elemental densities on material properties. Three typical numerical examples are employed to show the effectiveness of the proposed method.

Keywords:

• topology optimization
• multi-objective optimization
• fuzzy multiple-attribute group decision making
• normalized exponential weighted criterion

Acknowledgements

This work is supported by the National Natural Science Foundation of China (grant nos 51175197 and 51121002) and the Open Research Fund Program (31115020) of the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, China.