Singularity Method in Boundary Value Problems in the Theory of Elasticity : Part I Theory

Abstract

Betti's formula in the theory of elasticity which describes displacements by their boundary values and external forces acting on the boundary surface of the elastic body permits us to solve the boundary value problems by taking its boundary value as the integral equations and recently some authors report the usefulness of this method in numerical analysis. In the present report, in the same aim as the predecessor, authors develope various representation of the stress field, try numerical comutation and compare its usefulness with othor methods, especially with the finite element one in the plane stress problems. Conciudingly, this method is very much usefull especially for stress concentrasion problems making use of the proposed representation of the stress function.