Design of Axially Crushing Thin-Walled Square Tubes Using Compliant Mechanism Approach

Axially crushed thin-walled tubular structures are extensively used as energy absorbers in various automotive and aerospace applications because of their high energy absorption efficiency and long strokes. Various experimental and numerical studies in the past have revealed that a thin-walled square tube can under go mainly three modes of deformation, progressive crushing/buckling, dynamic plastic buckling and global bending depending up on the loading conditions and tube geometry among many factors. Out of these three, progressive crushing/buckling is the most desired mode of collapse for efficient energy absorption. Moreover, crushing starting from one end progressing systematically towards the other end is preferred because of availability of more space/material for plastic deformation without jamming resulting in increased peak forces. A thin square tube can show four possible modes of collapse during progressive crushing depending up on the ratio of width to thickness. The mean crush load for extensional mode of collapse is higher than the other three modes resulting in higher energy absorption during the overall crushing event. The crush behavior of thin square columns in case of oblique impact is highly dependent on the angle of impact. In the situations when impact angle is higher than a critical value, the mean crush load may drop by 40% than the axial crushing load because of global bending. In this paper, a novel approach based on compliant mechanism design which is extensively employed in topology optimization of MEMS is used to design the thin-walled square tubes. The ability of a compliant mechanism to transfer or transform displacement, force or energy from an input load location to the desired output locations is utilized to enforce the desired buckle zones in the axial member. A biologically inspired, gradient free hybrid cellular automata (HCA) method is used to synthesize compliant mechanisms with elemental thickness distribution governed by an enrgy like functional, mutual potential energy (MPE). Nonlinear explicit finite element code LS-DYNA is used to simulate quasi-static axial crushing of the thin square columns in this paper. Numerical results show that progressive crushing in a desired mode of collapse can be enforced in axial and oblique loading conditions using the proposed methodology.