Application of Stress Functions to Initial Stress Problems

Abstract

The governing equations of the linear initial stress problem are obtained from the pertinent equations of large deformation analysis. These equations are then cast in the framework of a variational statement. The functional has the incremental stresses and displacements as competing functions. However, in contrast to mixed formulations the displacement and stress fields are required to satisfy the equilibrium equations. This is done by invocation of classical stress functions and introduction of some new functions. The stationary conditions of the functional emerge as a set of compatibility equations. As such, the variational statement is referred to as the complementary energy principle, in spite of the presence of the displacements in its functional. The paper includes an example from 2D elasticity and a second example on buckling of cylindrical shells.