One Solution of Three-Dimensional Boundary Value Problems in the Couple-Stress Theory of Elasticity

Abstract

This paper describes a numerical approach for elastic boundary value problems in the linear, couple-stress theory on the basis of the “indirect fictitious-boundary integral method.” In this approach we introduce appropriate potentials corresponding to those for a concentrated force and a couple in an infinite medium, and reduce the problem to solving the simultaneous Fredholm type integral equations of the first kind. As an example, the stress concentration problem is analyzed for a circular cylinder with a semicircular annular groove under uniaxial tension. The results are obtained for various values of parameters such as Poisson’s ratio ν, characteristic length l, and the ratio ηr of bending, twisting moduli.