Torsion of cylindrical shafts has been a topic in the classical theory of elasticity for a long time (Timoshenko and Goodier, 1970). The stiffness of a cylindrical shaft under torsional loading is often of interest in the study of torsion problems. Therefore, the uniform (St. Venant) and non-uniform torsion problem of structural components has long been the subject of theoretical and practical ...

The relative mean square error in the three-dimensional stress field predicted by classical plate theory is shown to be OQi/L^)2, where h is the plate thickness and Lj. is a mean square measure of the wavelength of the midplane deformation pattern. This improves a recent result of Nordgren who obtained a relative error estimate of 0(h/L*). The improved error estimate, which, like Nordgren's, is...

The question of ‘generalization’ to finite strains of the constitutive relations of infinitesimal strain theory of elasticity, and classical elasto-plasticity with isotropic and kinematic hardening, is critically examined. Simple generalizations, which lead to physically plausible material behaviour, are presented. The current controversies surrounding (i) the choice of stress-rate in the above...

We examine some elementary interpretations of the classical theorem of CLAPEYRON in linear elasticity theory. As we show, a straightforward application of this theorem in the purely mechanical setting leads to an apparent paradox which can be resolved by referring either to dynamics or to thermodynamics. These richer theories play an essential part in understanding the physical significance of ...

The absence of conventional long range order in the classical two dimensional xy model is introduced. Two main types of excitations of this model, spin wave and vortices, are analyzed in the framework of generalized theory of elasticity. The Hamiltonian is then mapping onto the two dimensional Coulomb gas model and then critical temperature of the Kosterlitz-Thouless transition is located by a ...

We investigate a longitudinally loaded elastic nanorod inside a cylindrical channel and show within the context of classical elasticity theory that the Euler buckling instability leads to a helical postbuckling form of the rod within the channel. The local pitch of the confined helix changes along the channel and so does the longitudinal force transmitted along the rod, diminishing away from th...

Higher order gradient elasticity theories are widely applied to determine the wave propagation characteristics of micro-sized structures. The novelty this paper, firstly, is using Second Strain Gradient (SSG) theory explore mechanism a 2D beam grid. strong formulas continuum model including governing equations and boundary conditions derived by Hamilton principle. Then, valuable long-range Latt...