Sequential approximate optimization of composite structures

Abstract

The design of composite structures is of relevance in many fields of engineering (civil, naval, aerospace, automobile, etc.) and as such has become an active research field. To fully explore the benefits of using composite materials, optimization techniques are often needed. However, the computational cost of the structural analyses may become a hindrance for the optimization process. This is especially critical when dealing with bio-inspired algorithms, where a high number of trial designs are typically employed. Thus, surrogate models are a valuable alternative to help reduce computational cost and enable the optimization of complex structures. In this work, two surrogate models were studied: Radial Basis Function (RBF) and Kriging. Both surrogate models were used in association with an optimization technique known as Sequential Approximate Optimization (SAO), in which the approximate response surface is continuously updated and improved by the addition of new points in the design space. For that matter, two infill criteria were assessed: the Expected Improvement (EI) and the Weight Expected Improvement (WEI). Both use the Particle Swarm Optimization to maximize their acquisition functions. To evaluate the structural response of the composite structures, the Isogeometric Analysis (IGA) was employed. A comparison between the SAO algorithms was carried out in terms of accuracy, efficiency, and robustness. The implementation was validated using a set of numerical examples from the literature. The examples include different types of structures using functionally graded and laminated composite materials. Results show the efficiency of the proposed algorithms and highlight the impact of the choice of the Infill Criterion on their performance. An expressive reduction in the number of High-Fidelity (HF) evaluations was obtained compared to traditional optimization, saving a significant amount of processing time. This is particularly promising when the structural analysis involves refined meshes or the consideration of nonlinear behaviour. In general, the RBF consistently provided the fastest surrogate model building and updating processes, while Kriging provided more accurate results with fewer HF evaluations in a wide range of applications.