Free Contact Between Plate and Sagged Support Under Uniformly Distributed Load

This paper deals with the advancing contact between a rectangular plate simply supported on the two opposite edges and free on the others and an internal line sagged located along the center under uniformly distributed load. The finite Hankel transform method is used and the correct singularity is introduced at the tips of contact. The problem is formulated as dual series equations and reduced to an inhomogeneous Fredholm integral equation of the second kind in term of an unknown auxiliary function which can be solved numerically by using Simpson’s rule. The deflection, bending moment, and support reaction of the plate are expressed in the analytical form and presented graphically.

Keywords: Advancing Contact, Fredholm Integral Equation, Hankel Transform, Rectangular Plate, Analytical Solution, Singularity

Corresponding author: E-mail: ikraomol@kmutt.ac.th