Bending of a uniformly loaded square plate resting on unilateral edge supports

Abstract

The objectives of this paper are to analyze the bending behaviors of unilaterally simply supported square plate subjected to the uniformly distributed load, and to examine the extent of receding contacts between the plate and the unilateral supports. In the present problem the mixed boundary conditions exist along the plate edges, which can be written in the form of dual series equations. These equations are further reduced to determine the solution of inhomogeneous Fredholmintegral equation of the second kind for an unknown auxiliary function by using the finite Hankel integral transform techniques.Numerical results concerning the extent of receding contact, deflection, bending moment, twisting moment, and support reaction of the plate are given and also compared with the results obtained by other available techniques. From investigations, the conclusions can be stated that (i) the method used is found to be efficient for solving the problem considered, (ii) the extent of contact is independent of the level of loading, but dependent on the values of Poisson’s ratio of the plate, and (iii) the support reactions are proportional to the applied load.

Keywords

• dual series equations
• Fredholm integral equation
• Hankel integral transform
• mixed boundary conditions
• plate bending
• receding contact