# Mathematical Solutions for Bending of Uniformly Loaded Rectangular Plates with Mixed Edge Conditions

## Abstract

The present paper deals with the method of finite Hankel integral transforms for solving two specific cases of uniformly loaded rectangular plate simply supported on two opposite edges, and mixed between partially simply supported and free on the third edge where the remaining fourth edge may be specified by: (a) clamped support or (b) free support. The mathematical solution for the problems analyzed can be written in terms of single Fourier series satisfying the fourth-order partial differential equation governing to the plate behaviors. Therefore, the mixed boundary conditions on the third edge are formulated through dual-series equations, which can be reduced to determining the solution of inhomogeneous Fredholm integral equation of the second kind for the unknown auxiliary function. The most important consideration is that the inverse-square-root moment singularities are taken into account in the analysis at the points of transition from a simple support to a free edge and treated analytically. The solutions of integral equation are evaluated numerically for two different cases of the plate. The obtained results are demonstrated graphically and also given numerically in tabular form for assessing other analytical or numerical methods.

## Article Details

Section
Research Articles

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