Elastically homogeneous and isotropic material. Two independent constants. Plane Elastostatic Problems Prismatical cylinder subject to axially uniform, transverse loads only, and zero axial displacement. Body is in state of plane strain . Lecture 17 Assume stresses are given by taking certain partial derivatives of a scalar function of the lateral coordinates.
Stresses satisfy equilibrium equations.
Substitute stresses in the one governing stress compatibility equation to obtain biharmonic equation in the scalar function, now identified as Airy stress function . Another case, thin body in nearly plane stress state. Assume stresses and strains are nearly two-dimemsional. Assume again stresses given by Airy stress function. Substitute stresses in stress compatibility equation in lateral coordinates to obtain biharmonic equation in the Airy stress function.