Multi-objective optimization of a multi-cellular aluminum extruded crush rail subjected to dynamic axial and oblique impact loading conditions

Abstract

This work presents a multi-objective shape optimization study of a multi-cellular aluminum extrusion subjected to dynamic axial and oblique (20° angled) impact loading conditions. Finite element models are developed, validated with experimental data, parameterized, and used to exhaust the design space using a full factorial design of experiments. An analysis of different energy absorption characteristics, such as axial and oblique mean crush force, crush efficiency, and oblique impact coefficient, are presented. A multi-objective optimization problem is defined to generate new solutions that dominate a baseline profile in all aspects of performance, which produced a geometry with up to 16% improvements in energy absorption. The parametric study is used to define the “true” Pareto front, which is the set of non-dominated designs and the solution to the optimization problem. The response surface methodology (RSM) is used to perform the multi-objective optimization analysis. The traditional RSM approach is compared to an adaptive surrogate-assisted response surface method (ASA-RSM) in their speed and ability to identify the true Pareto front correctly. Using the traditional metamodel constraint, the traditional RSM approach could only identify 18% of the true Pareto front using up to 8% of the design domain. After relaxing the constraint, the traditional RSM approach still required approximately 63% of the entire domain to identify 67% of the true Pareto front accurately. In comparison, the ASA-RSM approach was able to identify 84.5% of the true Pareto front using 42% of the entire domain. In some instances, the ASA-RSM approach correctly identified 100% of the true Pareto front by using as little as 18% of the domain. However, the ASA-RSM approach’s peak performance is dependent on the initial sampling and resulting metamodel. This study provides a comprehensive understanding of the performance gains of multi-objective optimization in the application of structural crashworthiness considering various loading conditions.