Optimal Design of Nonlinear Multimaterial Structures for Crashworthiness Using Cluster Analysis

Abstract

This study presents an efficient multimaterial design optimization algorithm that is suitable for nonlinear structures. The proposed algorithm consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization. The conceptual design is generated using a structural optimization algorithm for linear models or a heuristic design algorithm for nonlinear models. Then, the conceptual design is clustered into a predefined number of clusters (materials) using a machine learning algorithm. Finally, the global optimization problem aims to find the optimal material parameters of the clustered design using metamodels. The metamodels are built using sampling and cross-validation, and sequentially updated using an expected improvement function until convergence. The proposed methodology is demonstrated using examples from multiple physics and compared with traditional multimaterial topology optimization method. The proposed approach is applied to nonlinear, multi-objective design problems for crashworthiness.

Design for Crashworthiness of Categorical Multimaterial Structures Using Cluster Analysis and Bayesian Optimization

“…This work introduces a novel cluster-based structural optimization (CBSO) method for the design of multimaterial, nonlinear structural optimization problems. Integral to this work is the use of clustering analysis and metamodel-based global (Bayesian) optimization, which was previously introduced by the authors [36,37]. Contributions of the present work include: (i) the derivation of a new cluster validity index for structural optimization that improves the clustering of the conceptual Page 3…”

“…Cluster analysis has been implemented in structural optimization to reduce the computational cost of the optimization algorithm [21] and to reduce the dimension of the design space [4,35,36,37]. Using a modified p-norm distance, stress functions have been grouped to reduce the number of constraints in stress-constrained topology optimization [21].…”

“…Step 1: Conceptual design generation. In order to trigger a progressive collapse on the S-rail, principles of topology optimization of compliant mechanisms [47,44] are applied to the design of thin-walled structures [6,36]: given the displacement of prescribed input ports, the objective is to find the thickness distribution that maximizes the displacement of prescribed output ports. The input ports are prescribed on the S-rail at the contact nodes with the rigid wall.…”

Cluster-Based Optimization of Cellular Materials and Structures for Crashworthiness

“…The basic cluster-based structural optimization approach involves three design steps: conceptual design generation, clustering, and metamodel-based global optimization. The method is presented in detail in [26] and summarized in this section for clarity.…”

“…The objective of this work is to propose a cluster-based optimization method for the optimal design of cellular materials and structures that involving nonlinear dynamic crashworthiness analysis. The proposed method builds upon a cluster-based structural optimization approach previously presented by the authors [26]. The basic approach consists of three steps: conceptual design generation, clustering, and metamodel-based global optimization.…”