Keywords: exact strip, relative stiffness, initial post-buckling stage, Von-Kármán's compatibility and equilibrium equations.

Prismatic plates and plate structures are often employed in situations where they are subjected to in-plane compressive loading. Thus it is important to accurately predict the buckling and post buckling behaviour of such structures. Ovesy et al. [1,2,3] have developed a semi-energy post-local-buckling finite strip method in which the out-of-plane displacement of the finite strip is the only displacement which is postulated by a deflected form.

This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of channel section struts. The strip is developed based on the concept that it is effectively a plate. The present method, provides an efficient and extremely accurate buckling solution. 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 channel section struts buckling behaviour 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. It is noted that in the present method, only one of the calculated out-of-plane buckling deflection modes, corresponding to the lowest buckling load, i.e. the first mode is used for the initial post-buckling study. Thus, 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 is used together with a consideration of the total strain energy of the structure. 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 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 method is subsequently applied to analyze the initial post-buckling behaviour of some representative channel sections.

1

H.R. Ovesy, J. Loughlan, S.A.M. Ghannadpour, "Geometric Non-Linear Analysis of Thin Flat Plates Under End Shortening, Using Different Versions of the Finite Strip Method", Int. J. of Mech. Sci., 47, 1923-1948, 2005. doi:10.1016/j.ijmecsci.2005.07.008

2

H.R. Ovesy, J. Loughlan, S.A.M. Ghannadpour, "Geometric Non-Linear Analysis of Channel Sections Under End Shortening, Using Different Versions of the Finite Strip Method", Comput. and Struct., 84, 855-872, 2006. doi:10.1016/j.compstruc.2006.02.010

3

H.R. Ovesy, J. Loughlan, S.A.M. Ghannadpour, G. Morada, "Geometric Non-Linear Analysis of Box Sections Under End Shortening, Using Three Different Versions of the Finite Strip Method", Thin-Walled Struct, 44, 623-637, 2006. doi:10.1016/j.tws.2006.05.006

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