Stress Solution of Multiple Elliptic Hole Problem in Plane Elasticity

Abstract

Using Schwarz’s alternating method and Muskhelishvili’s complex variable function techniques, this paper presents an iterative algorithm method for the effective and accurate calculation of the stresses in an elastic solid of infinite extent containing multiple elliptic holes and subject to external loading at the infinity. The elliptic holes can have different dimensions and locate at any points while their axis orientations must be orthogonal. The proposed iterative algorithm method is based on the approximation of the resultant force vector on each elliptic hole boundary as a series of complex variable. As a result, exact closed-form analytical stress solutions can then be obtained for the solid with a single elliptic hole whose boundary is subject to the reverse resultant force vector in the forms of complex series. The numerical results presented in the paper show that the iterative solution converges quickly and stably. The proposed convergent criterion ensures the satisfaction of the required accuracy of the stress results. The stress concentration at elliptic holes can then be evaluated with high accuracy.