Araki, T. and Shibutani, Y., "Effect of Loading Rate Dependence on Unstable Behavior of Thin-Shell Structured Beams under Axial Compression- Elucidation of Mechanism and Effect of Beam Aspect Ratio on Loading Rate Dependence," SAE Int. J. Passeng. Cars - Mech. Syst. 5(2):769-777, 2012, https://doi.org/10.4271/2012-01-0554.
The thin-shell structured beams that are used extensively in the vehicle body need to satisfy both strength requirements for crash safety and demands for weight reductions for environmental friendliness. This study focused on the loading rate dependence of reaction force, especially the maximum value, which is generated in thin-shell structured beams as a result of axial force inputs in a frontal crash. The mechanism generating the reaction force was made clear through a comparison with classical Euler buckling(1) and von Karman's effective width expression(2). It was observed that a square cross section displays markedly large loading rate dependence, which can be approximated well by considering the effect of inertial force in the high loading rate region and by von Karman's effective width solution in the low loading rate region. Essentially, this dependence is governed by Euler buckling. When the length of two sides of a square cross section was fixed and the length of the other two sides was varied, it was found that von Karman's effective width solution approximated the overall reaction force reasonably well. Large variation in the aspect ratio of the beam, however, caused greater approximation error. That was shown to be influenced by the change in the order of Euler buckling caused by variation in the constrained state of each side at the corners of the beam.