Multiobjective robust optimization for crashworthiness design of foam filled thin-walled structures with random and interval uncertainties

Abstract To improve crashing behavior of aluminum foam-filler columns design optimization has proven rather effective and been extensively used. Nevertheless, an optimal design could become less meaningful or even unacceptable when some uncertainties present. Parametric uncertainties are often treated as random variables in conventional robust optimization. Taking foam filled thin-walled structure as an example, which could also exhibit probabilistic and/or bounded nature of uncertainties, it may be more appropriate to describe them with hybrid uncertainties by using random variables and interval variables. Furthermore, evaluation of product quality often involves a number of criteria which may conflict with each other. To address the issue, this paper presents a multiobjective robust optimization to explore the design problems of parametric uncertainties involving both random and interval variables in foam filled thin-walled tube, in which specific energy absorption (SEA) and peak crushing force are considered as the design objectives and the average crash force is considered as the design constraint. A nesting optimization procedure is proposed here to solve the multiobjective robust optimization problem. In the outer loop, the Non-dominated Sorting Genetic Algorithm II (NSGA-II), is implemented to generate robust Pareto solution. In the inner loop the Monte Carlo simulation is performed to evaluate the impact responses of the mixed uncertainties to the robustness of optimized design. The example demonstrates the effectiveness of the proposed robust crashworthiness optimization involving both random and interval variables.