Explicit Solutions for Circular Plates With Discontinuous Axisymmetric Loads and Overhung Supports

Abstract

Well-known methods exist for the solution of problems involving axisymmetric loading of thin circular plates. Unfortunately, these methods result in rather tedious algebraic and numerical work when the loads are concentrated or piecewise continuous. In such cases, the standard procedure is to divide up the plate into a number of annular regions, and to piece together a solution by matching deflections, slopes, and bending moments at points of load discontinuity. In this paper, a method of solution is presented which avoids the need to patch or match. Instead, explicit solutions are given for deflections, moments, etc., in terms of well-defined definite integrals of the prescribed loading functions (both continuous and discontinuous loading patterns are handled with equal ease). Apart from a reduction in tedium, the proposed method lends itself particularly well to the solution of statically indeterminate axisymmetric problems of circular plates and to numerical evaluation of solutions by digital computers. It is pointed out that in many cases, even if tables of influence coefficients are available, the proposed method offers greater computational conveniences than do the tables. The method is illustrated by some problems involving plates with overhung edges. This type of boundary condition, although seldom discussed in the literature, is particularly important because it is impossible to simulate, in practice, a truly simple support without providing a certain amount of overhang.