Stress concentration analysis of an arbitrary shape hole coated by a functionally graded layer

Based on theory of the complex variable functions, the analysis of stress concentration in a homogeneous plate with an arbitrary shape hole coated by a functionally graded layer is presented. By using the method of piece-wise homogeneous layers and the technique of conformal mapping, the general solution for the functionally graded layer with normal arbitrary material properties is obtained as the plate is subjected remote uniform loads. The influences of functionally graded layer on the stress distributions around the holes with various shapes such as triangle, square, rectangle etc. are discussed in detail by numerical examples. It is shown that the stress concentration around an arbitrary shape hole can be successfully decreased by choosing proper change ways of elastic modulus along normal direction in the layer. The results for some special cases are compared with previous literatures and found in good agreement.