in this paper, the stability characteristics of single-walled carbon nanotubes (swcnts) under the action of axial load are investigated. to this end, a nonlocal flügge shell model is developed to accommodate the small length scale effects. the analytical rayleigh-ritz method with beam functions is applied to the variational statement derived from the flügge-type buckling equations. molecular dy...

In this article, classical plate theory (CPT) is reformulated using the nonlocal differential constitutive relations of Eringen to develop an equivalent continuum model for orthotropic triangular nanoplates. The equations of motion are derived and the Galerkin’s approach in conjunction with the area coordinates is used as a basis for the solution. Nonlocal theories are employed to bring out the...

elastic solutions applicable to single underground openings usually suffer from geometry related simplification. most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. d-shape or horse-shoe shape tunnels and others with arched roof and floor are examples of the later category (one symmetry axis). in the present...

The peridynamic model of solid mechanics is a nonlocal theory containing a length scale. It is based on direct interactions between points in a continuum separated from each other by a finite distance. The maximum interaction distance provides a length scale for the material model. This paper addresses the question of whether the peridynamic model for an elastic material reproduces the classica...

In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the L2 norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non–interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formula...

The elastic properties of a molecule of duplex DNA are strongly dependent on nucleotide sequence. In the theory developed here the contribution c of the nth base-pair step to the elastic energy is assumed to be given by a function c̃ of six kinematical variables, called tilt, roll, twist, shift, slide, and rise, that describe the relative orientation and displacement of the nth and (n11)th base ...

Elasticity theory provides an accurate description of the long-wavelength vibrational dynamics of homogeneous crystalline solids, and with supplemental boundary conditions on the displacement field can also be applied to abrupt heterojunctions and interfaces. The conventional interface boundary conditions, often referred to as ‘‘connection rules,’’ require that the displacement field and its as...

c = c = c . (2) 1 We use the notation of Schouten [9]. Symmetrization over two indices is denoted by parentheses, A(ij) := (Aij + Aji)/2!, antisymmetrization by brackets, B[ij] := (Bij − Bji)/2!. The analogous is valid for more indices, as, e.g., in (13): c i[jk]l = (c − c)/2!. If one or more indices are exempt from (anti)symmetrization, they are enclosed by vertical bars, as, e.g., in (12), c ...

This article argues that the difference between poor countries and rich countries has to do with governance rather than resources, emphasizing the importance of public administration in explaining economic success and failure. Political elasticity (PE) theory is introduced for the analysis presented here, including the following terminology: (1) political elasticity, (2) political inelasticity,...

theory, Applied Acoustics, Volume 70, Issue 5, May 2009, Pages 730-736, ISSN 0003-682X, http://dx.doi.org/10.1016/j.apacoust.2008.09.003. 1 Sound transmission prediction by 3-D elasticity theory Changzheng, Steven R. Nutt 1. Department of Chemical Engineering and Materials Science, University of Southern California, 3651 Watt Way, VHE 602, Los Angeles, CA 90089-0241, United States Abstract: The...