Stability of geometrically imperfect struts with Ramberg–Osgood constitutive law

Abstract

Both the initial geometrical imperfections and material nonlinearity have great influence on the stability of the struts. In this paper, an analytical approximate solution of the post-buckling behavior of the geometrically imperfect struts with pinned–pinned ends under axial compression is obtained. The struts are made of aluminum alloys, and its constitutive relation conforms to the Ramberg–Osgood law. The Ramberg–Osgood type constitutive relation is extended by Taylor series to facilitate its application. A theory based on Euler–Bernoulli hypothesis is applied to establish the nonlinear equilibrium equations of the aluminum alloy struts. The analytical approximate solutions of the nonlinear equilibrium equations are derived by the harmonic balance method for the first time. Moreover, numerical solutions are obtained by finite element analysis for comparison. By comparing with the numerical solution, the accuracy of the analytical approximate solution proposed in this paper is verified in the case of small strain. The effects of material nonlinearity and initial geometrical imperfections on the post-buckling equilibrium path of the aluminum alloy struts are analyzed by the proposed analytical approximate solution.