Applied Mathematics and Mechanics

, Volume 12, Issue 9, pp 871–879

# The general solution for axial symmetrical bending of nonhomogeneous circular plates resting on an elastic foundation

• Ji Zhen-yi
Article

## Abstract

In this paper, a new method, the exact analytic method, is presented on the basis of step reduction method. By this method, the general solution for the bending of nonhomogenous circular plates and circular plates with a circular hole at the center resting on an elastic foundation is obtained under arbitrary axial symmetrical loads and boundary conditions. The uniform convergence of the solution is proved. This general solution can also be applied directly to the bending of circular plates without elastic foundation. Finally, it is only necessary to solve a set of binary linear algebraic equation. Numerical examples are given at the end of this paper which indicate satisfactory results of stress resultants and displacements can be obtained by the present method.

## Key words

exact analytic method nonhomogeneous circular thin plate general solution

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