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

Abstract

Application of finite Hankel integral transforms to the problem of a uniformly loaded unilaterally supported rectangular thin plates, the solution of partial differential equation can then be reduced to two coupled Fredholm integral equations of the second kind that obtained from the coupled dual-series equations of mixed boundary conditions, and also together with two constraint integral equations resulted from both of zero corner force condition and compatibility of edge displacements near each plate corner that loses contact. Owing to the summation of many different infinite series in the kernels and inhomogeneous parts of equations for the requirements of attainable highest accuracy and reducible computational time, the modified mathematical manipulations are improved and required asymptotic expansion for large arguments of the Bessel and Struve functions is treated to accelerate the convergence of series rapidly. The latter is to avoid the undesirable lengthy computer runs in numerical computations. Consequently, this paper is devoted to demonstrate the mathematical description and numerical algorithms in order to solve the system of coupled integral equations.