Fredholm Integral Equation Solution for Rectangular Plate With Moment Singularity

This paper presents the finite Hankel transform method for a problem of rectangular plate clamped on the two opposite edges and simply supported on the remaining edges with an internal line support located along the center under uniformly distributed load. The proper singularity in the order of square root in moment is introduced at the tips of the internal support. The problem formulation is reduced to an inhomogeneous Fredholm integral equation of the second kind in term of an unknown auxiliary function which can be transformed to a set of algebraic simultaneous equations by using Simpson’s rule. The solution results provide the unknown auxiliary function of the problem and the physical quantities, namely the deflection and bending moment of the plate with various lengths of internal line support.

Keywords: Fredholm Integral Equation/ Hankel Transform/ Rectangular Plate/ Singularity

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