INTEGRAL-EQUATION APPROACHES FOR CURVED RIGID LINE PROBLEM IN AN INFINITE-PLATE

Possibilities for formulating the integral equation of the curved rigid line problem in an infinite plate are discussed and summarized. The relation between the obtained integral equations is also analyzed. A solution strategy for one type of the resulting integral equation is proposed. The basic idea is an approximation of the jump function of the resultant force along the rigid line by a polynomial multiplied by a weight function. The zero resultant force condition around the rigid line is thus satisfied automatically, and the Cauchy singular integral involved in the integral equation can be integrated in a closed form. A technique for evaluating the rotation of the rigid line is also investigated. After considering the interaction effect between the curved rigid lines, a system of integral equations for double rigid lines is also proposed. Finally, several numerical examples with the calculated stress singularity coefficients arc given.