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Finite Difference Numerical Solutions for Isotropic Rectangular Thin Elastic Plates with Three Edges Clamped and the Other Free  

Seo Seung-Nam (Coastal Engineering Research Department, KORDI)
Publication Information
Journal of Korean Society of Coastal and Ocean Engineers / v.18, no.3, 2006 , pp. 225-240 More about this Journal
Abstract
In order to calculate bending moments of rectangular plates with three edges clamped the other free subjected to both a uniform load and a triangular load, a finite difference equation for the non-dimensional governing equation are presented and numerical solutions with different aspect ratios and/or number of grid points are analyzed. The finite difference solutions are obtained by use of grid points up to 11,520 and the optimum grid points according to aspect ratios of the plate are presented as well. The obtained numerical solutions are shown to satisfy the given x moment boundary condition at the free edge, which can not be satisfied in Levy's analytical solutions and peculiar behaviour of the calculated moments is observed around the corners between the free edge and fixed ones. The numerical solutions of bending moments subjected to both a uniform load and a triangular load are compared with the corresponding analytical solutions which are shown in very good agreement on the solution domain except the neighborhood of the free edge.
Keywords
finite difference solution of rectangular plates; plates with three edges clamped and the other free; bending moment; convergence test;
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