ANALYTICAL SOLUTIONS OF KIRCHHOFF PLATE UNDER PARABOLIC LOAD USING DOUBLE FINITE SINE TRANSFORM METHOD
Abstract
The bending analysis of thin plates under parabolic load distribution has been scantily studied. This article presents the application of double finite sine transform method (DFSTM) for developing analytical solutions of thin plates under parabolic load distributed over the domain. The plate problem is assumed to be simply supported at all the four edges and rectangular in shape. The adopted DFSTM is suitable for the problem because the sinusoidal integral kernel functions satisfy the Dirichlet boundary conditions along the four edges    and  The DFSTM simplifies the problem from a partial differential equation (PDE) to an integral equation and ultimately to an algebraic equation in the transformed space. The general solution is obtained by inversion as a double Fourier sine series with infinite terms. The convergent properties of the double sine series allows the accurate solution of the problem using a few terms of the series. A one term truncation of the infinite series gave a center deflection solution for deflection that is 3.36% higher than the exact solution, previously found in the literature. A three term solution gave central deflection that is 3.00% higher than the exact solution
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KEYWORDS double finite sine transform method, Kirchhoff plate, integral kernel function, deflection, infinite sine series, bending moments.
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