ABSTRACT
The complex variable technique is one of the most elegant methods used extensively for two-dimensional plain strain or stress problem. Some salient features and basic preliminaries of the technique relevant to the contact and crack problem are mentioned without any details. Basic concepts of complex variable method of solution in infinite and semi-infinite medium have been introduced following Muskhelishvile, Green and Zerna. These are then used to solve the first fundamental problem of elasticity and derive the Green’s function in an infinite and semi-infinite half space. The integral equations for the contact problem are derived from the complex variable method. The singular integral solution is of standard Hilbert type. Muskhelishvile’s method is extensively used to solve the singular integral equation. In later section the stress is calculated for Hertzian pressure inside the half space. The line crack is posed and is directly solved as a singular integral solution. Also discussed is the line crack at the interface of two media by the transform method.
