On the stress functions in elastodynamics

Abstract

After a brief review on a theory of stress and stress functions in three-dimensional elastostatics, the author attempts to extend his consideration into the problem of elastodynamics. The stress is represented by the Riemann-Christoffel curvature tensor of a four-dimensional Riemannian space having the stress functions as the components of its metric tensor. From this basic recognition, a representation for stresses by ten stress functions is given. As one of the special cases, the expression for the stress the author used in the analysis of stress fields by moving dislocations is derived. Elementary expressions of the forms which are extensions of Morera's and Maxwell's stress functions are also derived from the general principle.