Antiplane strain in a nonlinearly elastic incompressible body

The stress-strain state of an incompressible cylindrical elastic body with antiplane strain under the action of potential forces and surface loading constant along the body is considered in a nonlinear formulation in actual variables. The stresses are expressed via the pressure and independent strains, the pressure is expressed via the force and elastic potentials, and nonlinear boundary-value problems are posed for strains (and displacements). Various methods for solving these problems are developed. For the nonlinear equations obtained, some analytical solutions containing free parameters are given, which can be used as a basis for solving particular problems. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 93–101, November–December, 2006.