Energy-absorbing analysis and reliability-based multiobjective optimization design of graded thickness B pillar with grey relational analysis

Abstract The functionally graded property structures, as a relatively novel configuration with higher material utilization rate, have been increasingly captured researcher's attention to date. In this paper, a functionally graded thickness (FGT) B pillar, which is characterized by a thicker wall thickness in load-bearing regions and a thinner wall thickness in other areas, is introduced to investigate its energy-absorbing and bending performance. And the reliability-based multiobjective optimization with grey relational analysis is carried out to solve infeasibility created by violation of constraint for conventional deterministic optimization via considering uncertainties of design parameters. Based on the validated finite element model, the FGT B pillar with three configurations and the corresponding uniform thickness (UT) B pillar are compared to explore the benefits of B pillar with different thickness layouts. And it reveals that the FGT B pillars, especially double functionally graded thickness (DFF) with different gradient exponents n for upper and lower part, exhibit superior crashworthiness to the UT B pillar. In addition, in order to research the distinctness between deterministic and reliable optimization in its entirety, multi-response optimization problems, coupling the high-accuracy Radical Basis Functions Network (RBF) and Monte Carlo Simulation (MCS), are established to produce a set of non-dominated solutions. The optimization results demonstrate that reliable Pareto fronts slightly are shifted away with diminishing performance from their deterministic counterpart attributable to its considered uncertainties, but significantly improve its reliability. Beyond that, a grey relational analysis combined with grey entropy is proposed to strike a desirable balance to the specific energy absorption (SEA) and the peak crashing force (Fmax) from Pareto-set under the condition of satisfied intrusion (Ma_In) constraint. Finally, the optimized result illustrates that the thickness variations of the upper and lower parts of the B column are subjected to concave and linear function distribution, respectively, which can provide some guidance for practical engineering with insightful design information.