An Investigation on Relative Post-Buckling Stiffness Variations of Symmetrically Cross-Ply Laminates

Abstract

In this paper, the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of symmetrically cross-ply laminates are presented. The so-called exact finite strip is developed based on the concept that it is effectively a plate. In the development process, the Von-Karman’s equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-of-plane buckling deflection modes. The investigation of thin flat plate buckling behavior is then extended to an initial post-buckling study with the assumption that the deflected form immediately after the buckling is the same as that obtained for the buckling. The post-buckling study is effectively a single-term analysis, which is attempted by utilizing the so-called semi-energy method. In this method, the Von-Karman’s compatibility equation governing the behavior of symmetrically laminated composite plates is used together with a consideration of the total strain energy of the plate. Through the solution of the compatibility equation, the in-plane displacement functions are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. These in-plane and out-of-plane deflected functions are then substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficient. The developed method is subsequently applied to investigate the relative post-buckling stiffness variations of some representative thin symmetric cross-ply laminates for which the results are also obtained through the application of a semi-analytical finite strip method.