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This work proposes a new method to design crashworthiness structures that made of functionally graded cellular (porous) material. The proposed method consists of three stages: The first stage is to generate a conceptual design using a topology optimization algorithm so that a variable density is distributed within the structure minimizing its compliance. The second stage is to cluster the variable density using a machine-learning algorithm to reduce the dimension of the design space. The third stage is to maximize structural crashworthiness indicators (e.g., internal energy absorption) and minimize mass using a metamodel-based multi-objective genetic algorithm. The final structure is synthesized by optimally selecting cellular material phases from a predefined material library. In this work, the Hashin-Shtrikman bounds are derived for the two-phase cellular material, and the structure performances are compared to the optimized structures derived by our proposed framework.

In the past decades, automotive structure design has sought to minimize its mass while maintaining or improving structural performance. As such, topology optimization (TO) has become an increasingly popular tool during the conceptual design stage. While the designs produced by TO methods provide significant performance-to-mass ratio improvements, they require considerable computational resources when solving large-scale problems. An alternative for large-scale problems is to decompose the design domain into multiple scales that are coupled with homogenization. The problem can then be solved with hierarchical multiscale topology optimization (MSTO). The resulting optimal, homogenized macroscales are de-homogenized to obtain a high-fidelity, physically-realizable design. Even so MSTO methods are still computationally expensive due to the combined costs of solving nested optimization problems and performing de-homogenization.

The design optimization of thin-walled tubular structures is of relevance in the automotive industry due to their low cost, ease of manufacturing and installation, and high-energy absorption efficiency. This study presents a methodology to design thin-walled tubular structures for crashworthiness applications. During an impact, thin-walled tubular structures may exhibit progressive collapse/buckling, global collapse/buckling, or mixed collapse/buckling. From a crashworthiness standpoint, the most desirable collapse mode is progressive collapse due to its high-energy absorption efficiency, stable deformation, and low peak crush force (PCF). In the automotive industry, thin-walled components have complex structural geometries. These complexities and the several loading conditions present in a crash reduce the possibility of progressive collapse. The Hybrid Cellular Automata (HCA) method has shown to be an efficient continuum-based approach in crashworthiness design.

Structures with multiple materials have now become one of the perceived necessities for automotive industry to address vehicle design requirements such as light-weight, safety, and cost. The objective of this study is to develop a design methodology for multi-material structures accountable for vehicle crash durability. The heuristic topology synthesis approach of Hybrid Cellular Automaton (HCA) framework is implemented to generate multi-material structures with the constraint on the volume fraction of the final design. The HCA framework is integrated with ordered-SIMP (solid isotropic material with penalization) interpolation, artificial material library, as well as statistical analysis of material distribution data to ensure a smooth transition between multiple practical materials during the topology synthesis.

This paper introduces a design methodology to tailor the acceleration and displacement responses of a vehicle structure subjected to a dynamic crushing load. The proposed approach is an extension of the hybrid cellular automaton (HCA) method, through which the internal energy density is uniformly distributed within the structure. The proposed approach, referred here to as an extended HCA (xHCA) method, receives the suitable combinations of volume fraction and a finite element meta-parameter for which the algorithm synthesizes the load paths that allow the desired crash response. Lower meta-parameter values lead designs obtained by traditional optimizers, while larger values lead to designs obtained by the HCA method. Simultaneous implementation of multiple values of meta-parameters is presented here as a further development of xHCA method.

A common scenario in engineering design is the evaluation of expensive black-box functions: simulation codes or physical experiments that require long evaluation times and/or significant resources, which results in lengthy and costly design cycles. In the last years, Bayesian optimization has emerged as an efficient alternative to solve expensive black-box function design problems. Bayesian optimization has two main components: a probabilistic surrogate model of the black-box function and an acquisition functions that drives the design process. Successful Bayesian optimization strategies are characterized by accurate surrogate models and well-balanced acquisition functions. The Gaussian process (GP) regression model is arguably the most popular surrogate model in Bayesian optimization due to its flexibility and mathematical tractability. GP regression models are defined by two elements: the mean and covariance functions.