Static and dynamic interactive buckling of isotropic thin-walled closed columns with variable thickness

The present paper deals with static and dynamic analysis of interactive buckling of thin-walled closed columns with variable thickness subjected to in-plane constant and/or pulse loading. This investigation is concerned with thin-walled structures with corners bevelled at the angle of 45° under axial compression. The plate model is adopted for the structures. The material, all plates are made of, is subject to Hookeʹs law. The structures are assumed to be simply supported at the ends. The differential equations of motion have been obtained from Hamiltonʹs principle. In this paper the static solution has been obtained by Koiterʹs asymptotic method in the second-order approximation. The study is based on the numerical method of the transition matrix using Godunovʹs orthogonalization. The interaction of an overall mode with two local modes having the same wavelength has been considered (i.e. three-mode approach). The nonlinear equations of dynamic stability are solved with the Runge–Kutta method. The calculations are carried out for settled imperfections.