An asymptotic solution for the large deflection of a circular plate with a central hole

Abstract

A linear asymptotic differential equation is derived in this work which closely approximates the deflection of a circular plate with a central hole for large values of the load parameter. This equation, therefore, replaces the exact non-linear von-Karman differential equation which results from the vertical force summation. The solution to the above equation may be used as an initial iterate to the numerical solution technique (hereafter referred to as the ‘exact’ solution) or may be used as a good engineering approximation in the useful load range. For a particular geometric configuration, an overlap of the linear (small deflection) solution and the asymptotic (large deflection) solution can result. This will eliminate the necessity of employing the exact solution. Numerical results are presented which compare the exact deflections with those obtained from the asymptotic solution.