Stress analysis of a functional gradient material plate with a circular hole under symmetric loads

摘要

This paper is to study the stress distribution of a functional gradient material plate with a circular hole under symmetric load. With using the method of homogenized layer and neglecting the thermal effects on the structure, the solution for the stress distribution of the functional gradient material plate having radial arbitrary elastic modulus is derived based on the known results of a single thick layer cylinder structure, and the continuous conditions of stress and displacement along the interfaces. When the number of the layer N → ∞, one can obtain an exact solution. But, since the N is taken as a finite number in general cases, so only an approximate solution can be presented. As an example, a functional gradient material plate with different radial elastic modulus is selected for numerical calculation. It is shown that the stress is greatly reduced as the radial elastic modulus increased, and moreover the stress level varies when the radial elastic modulus increased in different ways. Thus, it can be concluded that the stress around the circular hole in the functional gradient material plate can be effectively reduced by choosing the proper change ways of the radial elastic modulus.