Coupled integral equations for uniformly loaded rectangular plates resting on unilateral supports

Abstract

The present paper deals with the integral equations formulation through the method of finite Hankel integral transform techniques for solving the mixed boundary value problem of unilaterally supported rectangular plates loaded by uniformly distributed load. Due to the absent concentrated corner forces at all plate corners, the occurrence of mixed boundary conditions between a plate and the supports can be reduced from the coupled dual-series equations that resulted in using the Levy's approach for the plate deflection function to a set of two coupled integral equations of Fredholm-type. The highlight of problem is that the analyticalformulation explicitly considers the nature of the inverse-square-root shear singularities at the ends of unilateral supports in the plate loaded state.

On a treatment of coupled integral equations in nonlinear unilateral contact problem of plates

“…A B C D and also c W are determined from the boundary conditions. For this purpose, after performing (5), (6), (10), and (11) yields the system of four coupled series equations as follows [9]:…”

“…In the present paper, the objective is mainly emphasized on the numerical treatment of two coupled inhomogeneous Fredholm-type integral equations of the second kind which has been carried out successfully from the previous problem involving rectangular thin plates in unilateral receding contact with laterally loaded by uniform pressure [9] as shown in Figure 1.…”

The Laplace transform of derivative expressed by Heaviside function

“…Integral transform methods have been researched to solve many problems in the differential equations with initial or boundary conditions [1][2][3][4][5][6][7][8][9][10][11][12]. Laplace, Sumudu and Elzaki transforms are such typical things [3][4][5][6][7][8][9][10][14][15].…”