Nonlinear deformations of a cylindrical pipe with pre-stressed thin coatings

Abstract

The paper presents an exact solution for the problem of large deformations of torsion, axial tension–compression, and radial expansion or shrinkage of an elastic hollow circular cylinder equipped with pre-stressed elastic coatings. Surface coatings are modeled using the six-parameter nonlinear shell theory. The constitutive material of the cylinder is described by a three-dimensional nonlinear model of the isotropic incompressible body of the general form. Special boundary conditions describe the interaction of this material with thin coatings on the inner and outer surface of the pipe. Based on the solution obtained, numerical calculations were performed on the effect of preliminary stresses in coatings on the stress–strain state of a cylindrical pipe.

Universal deformations of ideal liquid crystal elastomers

“…Since these deformations automatically satisfy the equation of equilibrium, one only has to determine the parameters, and one can do so from macroscopic equilibrium and boundary conditions. This remarkable result explains the success of the semi-inverse method of Rivlin [29,28,30,31] and is the foundation of much work in finite elasticity since (see [24,43] for recent applications, and [41] for a discussion and extension to inhomogeneous bodies).…”