Optimal Design of S-Shaped Energy Absorbers Using Radial Basis Function Neural Networks and Differential Evolution Algorithm

Abstract

The presented study introduces a multiobjective optimization approach that combines numerical and surrogate modeling approaches in order to enhance the crashworthiness characteristics of thin-walled S-shape energy absorbers under axial impact loading. In particular, the optimization problem includes the maximization of energy absorption and minimization of peak crushing force by changing four important geometrical variables such as cross-section width, curvature angle, curvature radius, and wall thickness. To conduct the simulation of the progressive crushing process with large deformation, local buckling, plastic folding, and self-contact phenomena, a 3D finite element model was developed using ABAQUS/Explicit. These results have been verified against reference values, with the largest difference between theoretical and experimental values in relation to the absorbed energy and peak crushing force being equal to 2.86% and 0.75%, respectively. The database consisting of 58 absorbers was developed through numerical simulation. In turn, surrogate models based on Radial Basis Function (RBF) and Group Method of Data Handling (GMDH) were built from that database. It should be noted that GMDH showed excellent performance with determination coefficients equal to 0.9882 and 0.9725 for absorbed energy and peak crushing force, respectively. The developed surrogate models were later coupled with Differential Evolution (DE) to carry out the optimization analysis in order to construct the Pareto front. Eight non-dominated solutions were achieved, highlighting the natural trade-off between the energy absorption capacity and peak crushing force. Amongst the obtained solutions, one was selected as the compromise solution, which had an energy absorption of about 33,400 J and peak crushing force of about 8,713 N. The results reveal that the proposed integration of finite element modeling, neural-network surrogate model, and DE is quite effective in performing crashworthiness optimization of S-shaped energy absorber design at a significantly lower computational cost.