On the Solution of the Equilibrium Equations of Elasticity in General Curvilinear Coordinates

Abstract

A system of stress functions consisting of a harmonic vector and a harmonic scalar potential is introduced into the equations of equilibrium of an isotropic elastic body in arbitrary curvilinear coordinates and tensor form. The components of displacement and of the strew tensor me expressed in terms of these potentials and it is shown that the total number of independent components of the potentials is reducible to three.The tensor equations am then specialized to orthogonal curvilinear coordinates and expressions derived for the " physical " components of displacement and stress in terms of the stress functions. Reference is &e to the relation between the present approach and previous ones.