Nonlinear Post-Buckling Analysis of Isotropic Plates Using Finite Strip Methods

This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of isotropic plates. in the semi-analytical finite strip approach, all the displacements are postulated by the appropriate shape functions while in the development process of the full-analytical approach, the von-karman’s equilibrium equation is solved exactly to obtain the buckling loads and the out-of-plane buckling deflection modes. the investigation of plates buckling behaviour is then extended to the post-buckling study with the assumption that the deflected form after the buckling is the combination of first, second and higher (if required) modes of buckling. thus, the full-analytical post-buckling study is effectively a multi term analysis. in this method the von-karman compatibility equation is used together with a consideration of the total strain energy of the strut. through the solution of the compatibility equation, the in-plane displacement functions which are themselves related to the airy stress function are developed in terms of the unknown coefficients in the assumed out-of-plane deflection function. the in-plane and out-of-plane deflection functions are substituted in the total strain energy expressions and the theorem of minimum total potential energy is applied to solve for the unknown coefficients