The Stress Field Of An Infinite Plate With A Circular Inclusion Embedded With A Circular Hole: A Complex Variable Study

The issue of elastic mechanics is studied in 3D space and involved in the solution of the set of the partial differential equations with the proper boundary condition. It is generally troublesome to the solution for the set of the equations. The 3D problem can be treated in 2D space if the elastic body has specific shape and the external forces acting on the body are with specific characters. The stress and strain in 2D or plate are the formulations of two independent variables. Further, the solution of the formations can be reduced to the solution of Airy functions satisfying the bi-harmonic equation.These formulations then allow many powerful mathematical techniques available from the complex variable theory to be applied to the elasticity problem. By the implementation of complex variable notations, stress is derived as functions of complex variable potentials. These potentials must be made to satisfy the boundary conditions. However, due to the complexity of algebra involved in the problems, it is greatly difficult to get the solution by hand. The development of hardware and software of computers has made available symbolic algebra software packages such as MATHEMATICA, which provides the theoretical and technical support for the solution of such problems.In this thesis the stress field and displacement filed of an infinite plate with a circular inclusion embedded with a circular hole is investigated with complex variable method by calculating the potential functions. The analytical formulations are got and the simulations of the fields are performed by Mathematica for some specific domains.