An Investigation on the Three-Point Bending of Foam-Filled Double Tubes and Optimization of Parameters Using Response Surface Methodology

Document Type : Research Paper


1 Mechanical Engineering Department, Semnan University, Semnan, Iran

2 Faculty of Mechanical Engineering, Shahid Rajaee Teacher Training University, Tehran, 1678815811, Iran



In this research, the bending behavior of foam-filled double (FFD) tubes has been investigated. The aim was to obtain an optimized structure, which has the highest energy absorption capability with the lowest weight. Three-point bending tests have been performed on aluminum FFD tubes made of inner and outer tubes (1100 aluminum alloy) and a composite foam core (with A356 cast alloy base and 0.6 g/cm3 density). Furthermore, the finite element model of the tube bending has been constructed and its results have been validated using the experimental data. Afterward, the response surface methodology (RSM) has been used to (numerically) study the effect of inner and outer tubes’ diameters, inner and outer tubes’ thickness, and the foam density on the bending energy and the weight of the FFD tubes. By analysis of variance (ANOVA), the effectiveness of the studied parameters has been examined. Finally, the optimum values of the parameters, which result in the highest energy absorption in bending and the lowest weight of the FFD tube have been calculated using RSM. The optimization procedure led to a 141.4% increase in the absorbed bending energy and a 4.63% decrease in the weight of the FFD composite tube (in comparison to the initial design of the FFD tube).