Post-buckling analysis of plates and struts with initial imperfection

Abstract

Computation procedures for predicting the post-buckling responses of struts and plates with general initial imperfections, when subjected to progressive end shortening, are developed. Geometric non-linearity is introduced into the strain-displacement relations in a manner consistent with the von Karman assumptions. The set of non-linear equilibrium equations is solved by a Newton-Raphson procedure. In the post-buckling analysis if struts, the actual initial imperfection is simulated by suitable polynomial function, while the deformations are expressed by Fourier series. Transverse shear effect is included in the formulation. Comparisons with classical solutions without transverse shear and experimental results are presented. In the context of classical plate theory, a finite strip approach is developed for predicting the post-buckling response of plates under uniform end shortening. Out-of-plane initial imperfection is represented by a set of polynomial functions in the longitudinal direction, which are interpolated by some crosswise functions in the transverse direction. The approach is very general and is applicable to anisotopic plates and plates with general shapes of initial imperfection. Applications on perfectly flat plates and plates with various forms of initial imperfections are considered. It is demonstrated that both the post-buckling behaviors and deformed shapes are strongly influenced by the magnitudes and shapes of the initial imperfections.