The solution of certain loss of contact between a plate and unilateral supports

Abstract

This paper examines the loss of contact between a square plate and the unilateral supports under uniformly distributed load. Since the plate is rested on the unilateral supports, it will have the regions of lost contact between a plate and the supports due to the absence of restraining corner force at the plate corners. This leads to the mixed boundary conditions and these conditions are then written in the form of dual-series equations which can further be reduced to a Fredholm integral equation by taking advantage of finite Hankel transform technique. Numerical results are given for the deflections of free edge and deflections along the middle line of the plate with deferent values of the Poisson’s ratio. In addition, the deflection surface is also presented. From the investigation, it can be indicated that the loss of contact is decreased upon the increasing Poisson’s ratio.

Keywords

• plate
• receding contact
• mixed boundary conditions
• dual-series equations
• unilateral support
• Hankel transform
• Fredholm integral equation