Some solutions for a compressible isotropic elastic material

In this article we obtain closed-form solutions for thecombined inflation and axial shear of an elastic tube in respectof the compressible isotropic elastic material introducedby Levinson and Burgess. Several other boundary-value problemsare also examined, including the bending of a rectangular blockand straightening of a cylindrical sector, both coupled withstretching and shearing, and an axially varying twist deformation.Some of the solutions appear in closed form, others areexpressible in terms of elliptic functions.