A Circular Crack Under Asymmetric Loads and Some Related Integral Equations

A method of solution in terms of polynomials is developed for some integral equations that arise in connection with boundary-value problems for the circular disk. The key result is a Neumann series expansion of the kernel in terms of Gegenbauer polynomials. The method is developed in connection with the problem of a circular crack under general asymmetric loads and leads to explicit relations between the applied surface stresses and the crack opening. The method completely avoids the use of Abel integrals often associated with dual integral equations and is easily adapted to numerical calculations.