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Structural Engineering and Mechanics
  Volume 31, Number 2, January30 2009 , pages 181-210

An exact finite strip for the calculation of relative post-buckling stiffness of isotropic plates
H. R. Ovesy and S. A. M. Ghannadpour

    This paper presents the theoretical developments of an exact finite strip for the buckling and initial post-buckling analyses of isotropic flat plates. The so-called exact finite strip is assumed to be simply supported out-of-plane at the loaded ends. The strip is developed based on the concept that it is effectively a plate. The present method, which is designated by the name Full-analytical Finite Strip Method in this paper, 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 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. 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 semienergy method. In this method, the Von-Karman\'s compatibility equation governing the behavior of isotropic flat 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 which are themselves related to the Airy stress function are developed in terms of the unknown coefficient in the assumed outof-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 analyze the initial postbuckling behavior of some representative thin flat plates for which the results are also obtained through the application of a semi-analytical finite strip method. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is significantly promoted.
Key Words
    exact strip; relative stiffness; initial post-buckling stage; von-karman
H. R. Ovesy; Aerospace Engineering Department and Centre of Excellence in Computational Aerospace Engineering, Amirkabir University of Technology, Tehran, Iran
S. A. M. Ghannadpour; Space Engineering Department, Faculty of New Technologies and Energy Engineering, Shahid Beheshti University, G.C., Evin, 1983963113, Tehran, Iran

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