A hybrid multilevel method for simultaneous optimization design of topology and discrete fiber orientation

Abstract

This paper proposes a hybrid multilevel approach of simultaneous optimization design of topology and discrete fiber orientation for maximum stiffness design of constant-stiffness laminated plates. The lamination parameters are selected as the intermediate variables to overcome the local optima behaviors derived from directly optimizing fiber orientation. The hybrid multilevel method incorporates two different types of optimization techniques to benefits from the advantages of them. At the first level, lamination parameters and density are taken as the design variables, the method of moving asymptotes (MMA) is applied to obtain the optimal lamination parameter and topology shape simultaneously. At the second level, taking the discrete fiber orientation angles of individual layers as the design variables, a detailed lay-up design optimization considering some limitations on manufacturing is implemented by an improved direct simulated annealing (IDSA) algorithm. Thus, the hybrid multilevel optimization procedure can achieve a global optimum and obtain a faster convergence. Finally, Numerical examples are tested to illustrate and validate the proposed hybrid method.