Stresses in an elastic body under nonlinear antiplane deformation

The stress field in a cylindrical elastic body under antiplane deformation and certain constraints imposed on volume and surface forces is studied in a nonlinear formulation in actual-state variables. A boundary-value problem for independent stress components is formulated in Cartesian and complex variables, sufficient ellipticity conditions for this problem are indicated, and constraints on surface loading are imposed. Analytical solutions are given for linear and weak nonlinear elastic potentials. Similarity to a plane subsonic ideal-gas flow is established. An approximate method for the solution of the problem is developed.