Keywords: exact strip, moderately thick plates, initial post-buckling stage, relative stiffness, first-order shear deformation theory, Von-Karman's equations.

An exact finite strip for the buckling and initial post-buckling analysis of moderately thick plates is presented in this paper using first-order shear deformation theory (FSDT). The method presented, is designated by the name full-analytical finite strip method (FSM), provides an efficient and extremely accurate buckling and initial post-buckling solution. Ovesy and Ghannadpour [1,2,3,4] have developed a full-analytical FSM (F-a FSM) based on the classical plate theory (CPT) in which the Von-Karman's equilibrium equation is solved exactly and thus the buckling mode shapes and loads are obtained with very high accuracy. Then the obtained mode shapes are used in the post-buckling phase and the Von-Karman's compatibility equation is solved exactly and the in-plane displacements are derived.

In this paper the preceding method has been extended based on the FSDT. The Von-Karman's equilibrium set of equations for large deflection of a strip, with the assumption that the normal pressure is zero, is used based on the FSDT.

The analytical solution of this set of equations depends on the magnitudes of material properties, geometrical dimensions of the model and the applied compressive load. The buckling loads and mode shapes corresponding to the out-of-plane deflection and rotations functions have been obtained from a transcendental eigenvalue problem that is derived using the boundary conditions, moments and forces at the two unloaded edges.

An accurate initial post-buckling study can be extended with the assumption that the deflected form immediately after buckling is the same as that obtained for buckling.

With the solution of the Von-Karman's compatibility equation, the in-plane displacement functions which are related to the Airy stress function are developed in terms of the unknown coefficient in the assumed out-of-plane deflection function. The in-plane displacements obtained as well as out-of-plane displacements and rotations are used to develop the total strain energy expression. By solving the set of equations that is obtained from the minimum total potential energy theorem the unknown coefficients are obtained, thus the initial post-buckling behaviour is investigated.

1

S.A.M. Ghannadpour, H.R. Ovesy, "An exact finite strip for the calculation of relative post-buckling stiffness of I-section struts", International Journal of Mechanical Sciences, 50, 1354-1364, 2008. doi:10.1016/j.ijmecsci.2008.07.010

2

S.A.M. Ghannadpour, H.R. Ovesy, "The application of an exact finite strip to the buckling of symmetrically laminated composite rectangular plates and prismatic plate structures", Composite Structures, 89, 151-158, 2009. doi:10.1016/j.compstruct.2008.07.014

3

H.R. Ovesy, S.A.M. Ghannadpour, "An exact finite strip for the initial postbuckling analysis of channel section struts", Computers and Structures, 89, 1785-1796, 2011. doi:10.1016/j.compstruc.2010.10.009

4

H.R. Ovesy, S.A.M. Ghannadpour, "An exact finite strip for the calculation of relative post-buckling stiffness of isotropic plates", Structural Engineering and Mechanics, 31, 181-210, 2009.

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