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Abstract

This work presents the Galerkin-Vlasov method for solving the elastic buckling problem of Kirchhoff plate (length a and width b) under uniaxial uniform compressive load applied at the two opposite simply supported edges (x = 0 and x = a) with the edge y = 0 simply supported and the edge y = b free. Mathematically, the problem is a boundary value problem (BVP) represented by a partial differential equation (PDE) over the domain subject to boundary conditions at the plate edges. Upon suitable selection of basis functions the Galerkin-Vlasov method converts the domain equation to an integral equation, and ultimately to ordinary differential equations (ODE). The ODE is solved, and boundary conditions along y = 0, and y = b for the considered problem used to generate system of homogeneous equations in terms of the integration constants. The characteristic buckling equation is found as a transcendental equation from the condition for nontrivial solutions of the system of homogeneous equations. The roots of the transcendental equation obtained by computational software and iterative techniques are used to obtain the elastic buckling loads for the first two buckling modes, for various aspect ratios (a/b) and for Poisson ratio of m = 0.25. It is found that the critical elastic buckling load occurs at the first buckling mode, and the values of the critical elastic buckling loads computed are in close agreement with values obtained previously by Timoshenko.