Wang, T., Wang, L., Wang, Y., Zou, X. et al., "Multi-Criteria Optimization of Foam Reinforced Thin-walled Tube Shape under Crashworthiness Requirements," SAE Technical Paper 2015-01-1364, 2015, doi:10.4271/2015-01-1364.
The design of aluminum foam reinforced thin-walled tubes has garnered much interest recently due to the high energy absorption capacity of these tubes. As a new kind of engineering composite material, aluminum foam can hugely increase the crashworthiness capacity without sacrificing too much weight. In this paper, axisymmetric thin-walled hollow tubes with four different kinds of cross-sections (circular, square, hexagonal and octagonal) are studied to assess their performance for crashworthiness problems. It is found that the tube with square cross-section has the best crashworthiness performance under axial impact. To seek optimal designs of square aluminum foam reinforced thin-walled tubes, a surrogate modeling technique coupled with a multi-criteria particle swarm optimization algorithm has been developed, to maximize specific energy absorption (SEA) and minimize peak crash force (PCF). To improve the accuracy of the optimization process, meta-models of SEA and PCF were constructed using the response surface method and radial basis function method, respectively. Crash simulations carried out using LS-DYNA demonstrate that the optimal design has better crashworthiness characteristics than the baseline design. These results suggest that the proposed method can be of benefit in design optimization for other crashworthiness problems.