Multi-objective crashworthiness optimization of tapered thin-walled square tubes with indentations

This paper presents one and multi-objective crashworthiness optimization of the tapered thin-walled square tube with indentations. In this study, effects of cross section, thickness, taper angle, number and radius of indentations (as design variables) on the beam's energy absorption capability during crashes are investigated. The crashworthiness of models is evaluated using two metrics: The specific energy absorption per unit mass (SEA) and the ratio between the average and maximum crushing forces ( CFE = F avg / F max ). The optimum values of the number and radius of the indentations, the taper angle, the tube thickness and the cross section using a combination of response surface (RS) model, genetic algorithm and desirability function optimization are obtained. Multi-objective optimization of the tubes is performed by maximizing a composite objective including CFE and SEA. Analyses involved in this paper are undertaken using finite element models and solver (Abaqus). Also the computer program MATLAB is used to perform all the analyses and the optimization. Multi-objective optimization of the tubes showed that the tapered thin-walled square tubes with indentations have significantly, better crush performance in comparison to those without indentations. It is found that maximum CFE requires large number and radius of indentations, thickness, and cross section with small taper angle, while maximum SEA requires medium number of indentations and radius, large thickness and small taper angle and cross section. Also, the sensitivity of the design variables on the tapered square beam's crash behavior performance is analyzed. The objective functions, including SEA and CFE, were formulated using the Response Surface Method.