An equivalent stiffness (ES) method for initial design of tube-based energy absorbers under lateral quasi-static compression

A tube is often applied as an energy absorber in structures subject to impact loads. However, when several tubes are combined to absorb energy, how to arrange these tubes and match their dimensions has not been investigated. We provide a novel equivalent stiffness (ES) method for the initial design of tube-based energy absorbers, in which each tube is expressed by an equivalent spring with average post-buckling stiffness, and these springs are connected in series or parallel or hybrid. The plastic deformation and strain energy are distributed among them according to their relative ES value. The relationship between plastic energy and post-buckling stiffness is derived analytically and verified numerically. Finally, an application example is provided and the optimal tube arrangement and dimensions are obtained by combining the proposed ES method with an optimization code. The results demonstrate that this method can provide an initial design of tube-based energy absorbers efficiently.