A SURVEY OF NEW INTEGRAL-EQUATIONS IN PLANE ELASTICITY CRACK PROBLEM

The formulation of the integral equations in plane elasticity crack problem is presented in this review. Emphasis is laid on some proposals for formulating the Fredholm integral equation (FIE) and regularizing the existing singular integral equation (SIE) in the crack problem. Two kinds of regularization are suggested for the multiple crack problems. The first kind of regularization is obtained by the use of an appropriate substitution of the unknown functions in SIE while the second one is reached by operating some integral operator on SIE. Alternatively, the FIE will be obtained directly if one chooses the traction applied along the crack as the unknown function in the equation. For the curve crack problem, the resultant force function rather than the traction applied on the crack face is chosen as the right hand term in the resulting integral equation. Therefore, a weaker singular integral equation with logarithm kernel is obtainable. Some modified complex potentials (MCP) similar to the Green's function for solving the Laplace's equation are introduced. The MCP will provide possibilities for solving some relevant problems. It is proved that the proposed FIE for the crack problem is easier td compute. Miscellaneous problems, say, the thermally insulated crack problem, are also discussed.