An Efficient Series Term Truncation Strategy for the First-Order Perturbation-Based Robust Topology Optimization of Composite Structures

Abstract

This work focuses on the robust topology and discrete fiber orientation optimization of fiber-reinforced composites with spatially varying mechanical properties. The optimization problem in question is addressed for minimization of the robust compliance function, as formulated in closed form by employing the first-order perturbation method to perform the Stochastic Finite Element Analysis (SFEA) on the structural domain. For this class of optimization problems, a methodology is introduced aimed at reducing the overall computational effort required to solve them. Specifically, a strategy is proposed, designed to truncate the number of terms required in the first-order Taylor series expansion of the structural response. This truncation process is conducted for the state variables at each optimization iteration by performing a convergence analysis on the current value of the robust compliance function. By incorporating this strategy into the conventional robust topology and discrete fiber orientation optimization problem, its computational intensity is alleviated in two ways: firstly, via reducing the governing equations’ size in the SFEA , and secondly, by foregoing the computation of the Jacobian for the Taylor series terms excluded from the current iteration. Numerical examples are provided demonstrating the strategy's effectiveness across different levels of spatial variability in the material's mechanical properties.

Keywords: Topology optimization, fiber orientation optimization, robust compliance minimization, spatial material variability, first-order perturbation method, K-L series expansion