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To promote the progressive collapse of thin-walled vehicle structures and improve their energy-absorbing capabilities, designers allocate collapse initiators such as holes, grooves, humps, and creases. The use of some traditional origami patterns in pre-folded tubes has been particularly effective in this task. However, selecting the optimal origami pattern is a complex multidimensional combinatorial problem. This paper introduces a new origami pattern that triggers an extensional progressive collapse mode in a wide range of thin-walled tubes with a square cross-section. The parameters of the proposed pattern are optimized using a multi-objective Bayesian optimization algorithm to minimize the peak crushing force and maximize the mean crushing force. The crash simulations are supported by the commercial finite element solver Radioss. The optimized pre-folded origami structure depicts extensional progressive collapse under axial loads.

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.

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.