The plane problem of couple stress theory of elasticity for an infinite plane weakened by a finite number of circular holes

Abstract

Only problems on the stress concentration near a single round hole have been investigated [1 to 3] in the context of the plane problem of the theory of elasticity with couple stress. In the present paper we offer a method for solving plane problems of theory of elasticity with couple stress for a plane, weakened by a finite number of arbitrarily situated circular unconnected holes. It is shown that the problems are reducible to infinite systems of algebraic equations. The basic inequalities and relations required to prove the quasi-regularity of infinite systems and the uniqueness of the solution are obtained. The problem of two circular holes of equal size is discussed in detail. The quasi-regularity and uniqueness of the solution of the resulting infinite system of algebraic equations is proved under the following conditions: 1. (1) a self-balanced load is applied to the contours; 2. (2) the normal and tangential components are continuous functions whose first derivatives satisfy the Dirichlet condition; 3. (3) the distributed couples and first derivatives are continuous functions, while the second derivative satisfies the Dirichlet condition.