Comparison of parameterization schemes for solving the discrete material optimization problem of composite structures

Optimal design of composite structures can be formulated as an optimal selection of material in a list of different laminates. Based on the seminal work by Stegmann and Lund, the optimal problem can be stated as a topology optimization problem with multiple materials. The research work carries out a large investigation of different interpolation and penalization schemes for the optimal material selection problem. Besides the classical Design Material Optimization (DMO) scheme and the recent Shape Function with Penalization (SFP) scheme by Bruyneel, the research introduces a generalization of the SFP approach using a bi-value coding parameterization (BCP) by Gao, Zhang and Duysinx. The paper provides a comparison of the different parameterization approaches. It also proposes alternative penalization schemes and it investigates the effect of the power penalization. Finally, we discuss the solution aspects in the perspective of solving large-scale industrial applications. The conclusions are illustrated by a numerical application for the compliance maximization of an in-plane composite ply.