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

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.

Accurate Results for Free Vibration of Doubly Curved Shallow Shells of Rectangular Planform (Part.1)

A method is presented for determining the free vibration frequencies of doubly curved, isotropic shallow shells under general edge conditions and is used to obtain accurate natural frequencies for wide range of geometric parameters. Based on the shallow shell theory applicable to thin thickness shells, a method of Ritz is extended to derive a frequency equation wherein the displacement functions are modified to accommodate arbitrary sets of edge conditions for both in-plane and out-of-plane motions. In numerical computation, convergence is tested against series terms and comparison study is made with existing results by other authors. Twenty one sets of frequency parameters are tabulated for a wide range of shell shape and curvature ratio to serve as data for future comparison and practical design purpose.

Applicability and Limitations of Simplified Elastic Shell Theories for Vibration Modelling of Double-Walled Carbon Nanotubes

The applicability and limitations of simplified models of thin elastic circular cylindrical shells for linear vibrations of double-walled carbon nanotubes (DWCNTs) are considered. The simplified models, which are based on the assumptions of membrane and moment approximate thin-shell theories, are compared with the extended Sanders–Koiter shell theory. Actual discrete DWCNTs are modelled by means of couples of concentric equivalent continuous thin, circular cylindrical shells. Van der Waals interaction forces between the layers are taken into account by adopting He’s model. Simply supported and free–free boundary conditions are applied. The Rayleigh–Ritz method is considered to obtain approximate natural frequencies and mode shapes. Different aspect and thickness ratios, and numbers of waves along longitudinal and circumferential directions, are analysed. In the cases of axisymmetric and beam-like modes, it is proven that membrane shell theory, differently from moment shell theory, provides results with excellent agreement with the extended Sanders–Koiter shell theory. On the other hand, in the case of shell-like modes, it is found that both membrane and moment shell theories provide results reporting acceptable agreement with the extended Sanders–Koiter shell theory only for very limited ranges of geometries and wavenumbers. Conversely, for shell-like modes it is found that a newly developed, simplified shell model, based on the combination of membrane and semi-moment theories, provides results in satisfactory agreement with the extended Sanders–Koiter shell theory in all ranges.