Collaborative optimization design of Variable-thickness composite laminates using finite difference method and stochastic global search

Abstract

Variable-thickness design of fiber-reinforced composites is pivotal for lightweighting high-end aerospace equipment. However, traditional constant-thickness designs often fail to fully exploit material mechanical properties. Furthermore, existing optimization strategies often fail to adequately capture complex 2D and 3D composite behaviors, while deterministic search methods are prone to converging on local optima. To address these issues, this paper proposes a collaborative optimization method for variable-thickness laminates integrating the Finite Difference Method (FDM) and stochastic global search. The stabilized 2D FDM solver discretizes fourth-order partial differential governing equations to calculate deflection and stress fields of cantilever plates. The retention of key layers prior to random sampling, as part of a symmetric layer-dropping strategy, ensures diverse cutting patterns and helps avoid local optima. The results of the proposed method show good agreement with those obtained from finite element analysis. A comprehensive parametric study then provides distinct design recommendations: the optimal partition ratio lies between 0.45 and 0.65, and an optimal resin pocket length of 0.03L reduces the maximum stress by 55% relative to the 0.01L baseline. Ultimately, the optimized design balances lightweighting and deformation control, clarifies the performance potential of optimal layups, and provides analytical tools and practical guidelines for variable-thickness composite structures. As a result, it holds certain engineering value.