High accuracy postbuckling analysis of box section struts

Abstract

This paper presents the theoretical developments of two finite strip methods (i.e. semi-analytical and full-analytical) for the post-buckling analysis of some box section struts. 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-Kármán's equilibrium equation is solved exactly to obtain the buckling loads and the corresponding form of out-ofplane buckling deflection modes. The investigation of struts 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, which is attempted by utilizing the so-called semi-energy method. In this method the von-Kármán 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. It is noted that the Classical Plate Theory (CPT) is applied throughout the theoretical developments. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of these methods is significantly promoted.

Buckling and post-buckling behaviour of moderately thick plates using an exact finite strip

“…Then the first obtained mode shape is used in the postbuckling phase and the Von-Karman's compatibility equation is solved exactly to obtain the general form of in-plane displacement fields. Ghannadpour and Ovesy [19][20][21] have extended their exact method for non-linear post-buckling behaviour of isotropic plates and plate structures based on CPT by taking into account a combination of the first, second and higher (if required) modes of buckling and solving the Von-Karman's compatibility equation resulted from substituting the combined deflection function, thus, the post-buckling behaviour has been investigated with high accuracy. It is noted that a proper verification study is carried out in Ref.…”