Stress functions and internal stresses in linear three-dimensional anisotropic elasticity

Abstract

A stress function method is presented in order to give a general solution of the incompatibility problem of three-dimensional linear anisotropic elasticity theory. A relation between the internal stress tensor in terms of derivatives of a sixth-order stress function tensor will be derived. Using this formulation the so far open problem of the representation of the second-order stress function tensor by the fourth-order stress function tensor in anisotropic elasticity theory is solved in general.