Journal of Solid Mechanics
Volume:3 Issue: 1, Winter 2011

In this article, curvature effects on elastic thermal buckling of double-walled carbon nanotubes under axially compressed force are investigated using cylindrical shell model. Also, the small scale effect is taken into account in the formulation. The dependence of the interlayer van der Waals (vdW) pressure on the change of the curvatures of the inner and outer tubes at that point is considered. The effects of the surrounding elastic medium, curvature and the vdW forces between the inner and outer tubes increase the critical buckling load under thermal and axial compression loads, while small scale effect decreases it.

In this article, magneto-thermo-elastic stresses and perturbation of magnetic field vector are analyzed for a thick-walled cylinder made from polystyrene, reinforced with functionally graded (FG) single-walled carbon nanotubes (SWCNTs) in radial direction, while subjected to an axial and uniform magnetic field as well as a transient thermal field. Generalized plane strain state is considered in this study. The SWCNTs are assumed aligned, straight with infinite length. Two types of variations in the volume fraction of SWCNTs were considered in the structure of the FG cylinder along the radius from inner to outer surface, namely: functionally graded increasing (FG Inc) and functionally graded decreasing (FG Dec) which are then compared with uniformly distributed (UD) layouts. The constitutive equations of this type of reinforced polymeric cylinder are derived by Mori-Tanaka method. Following the introduction of a second order partial differential equation derived from the equations of motion and stress-strain relationships andsolving by a semi-analytical method, distribution of stresses and perturbation of magnetic field vector are obtained. Results indicate that maximum radial and circumferential stresses occur in FG Inc and FG Dec layouts, respectively. Maximum perturbation of magnetic field vector is not affected by UD layout.

In this paper, the general solution of steady-state two-dimensional non-axisymmetric mechanical and thermal stresses and mechanical displacements of a hollow thick cylinder made of fluidsaturated functionally graded porous material (FGPM) is presented. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the non-homogenous system of partial differential Navier equations, using the Complex Fourier Series and the power law functions method. The material properties, except of Poisson''s ratio, are assumed to depend on the radial variable r and they are expressed as power law functions.

One of the yet unresolved engineering problems is forecasting the creep lives of weldment in a pragmatic way with sufficient accuracy. There are number of obstacles to circumvent including: complex material behavior, lack of accurate knowledge about the creep material behavior specially about the heat affected zones (HAZ),accurate and multi-axial creep damage models, etc. In general, creep life forecasting may be categorized into two groups, viz., those that are based on microscopic modeling and others that are based on macroscopic (phemenological) concepts. Many different micro-structural processes may cause creep damage. The micro-structural processes highlight the fact that the creep damages can be due to cavity nucleation and growth. Dislocationcreep is another mechanism with micro-structural features such as sub-grain formation andgrowth, new phase formation, such as the Z phase, coarsening leading to the dissolution of the MX phase. This leads to the removal of pinning precipitates, which allow local heterogeneous subgrain growth, weakening due to this growth and also to the dissolution of the MX. These features normally lead to the earlier formation of tertiary creep and reduced life. Considering welded joints, the development of models for practical yet sufficiently accurate creep life forecasting based on micro-structural modeling becomes even more complicated due to variation of material in the base, weld and heat-affected-zone (HAZ) and variation of the micro-structure within HAZ and their interactions. So far, and until this date, none of the micro-structural models can forecast the creep life of industrial components with sufficient accuracy in an economic manner. There are several macroscopic (phemenological) models for creep life forecasting, including: time fraction rule, strain-fraction rule, the reference stress and skeletal stress method, continuum damage model, etc. Each of which has their own limitations. This paper gauges to a multi-axial yet pragmatic and simple model for creep life forecasting weldment operating at high temperature and subjected to an elastic-plastic-creep deformation.

In this study, based on nonlocal differential constitutive relations of Eringen, the first order shear deformation theory of plates (FSDT) is reformulated for vibration of nano-plates considering the initial geometric imperfection. The dynamic analog of the von Kármán nonlinear straindisplacement relations is used to derive equations of motion for the nano-plate. When dealing with nonlinearities, in the frame work of nonlocal theory, challenges are presented because of the coupling between nonlocal stress resultants and displacement terms. Governing equations are solved using differential quadrature method (DQM) and numerical results for free vibration of an imperfect single layered graphene sheet are presented.

The objective of this paper is to control the phase shifting by applying a bias DC voltage and changing the mechanical characteristics in electrostatically-actuated micro-beams. This problem can be more useful in the design of micro-phase shifters, which has not generally been investigated their mechanical behavior. By presenting a mathematical modeling, Galerkin-based step by step linearization method (SSLM) and Galerkin-based reduced order model have been used to solve the governing static and dynamic equations, respectively. The equilibrium positions or fixed pints of the system have been determined and the calculated static and dynamic pull-in parameters have been validated by previous experimental and theoretical results and a good agreement has been achieved. The frequency response of the system has been studied and illustrated that changing applied bias DC voltage affects the resonance frequency and maximum amplitude of the system vibrations. Then, phase diagram of the system for various damping ratio and excitation frequencies has been gained. It has been shown that by changing the bias DC voltage applied on the electrostatically-actuated micro-beam, which can be used as a varactor in phase shifter circuit, the stiffness of the micro-beam changes and consequently the phase shifting can be controlled. Finally, effect of the geometrical and mechanical properties of the micro-beam on the value of the phase shifting has been studied.

Hygrothermal analysis of laminated composite plates has been done by using an efficient higher order shear deformation theory. The stress field derived from hygrothermal fields must be consistent with total strain field in this type of analysis. In the present formulation, the plate model has been implemented with a computationally efficient C0 finite element developed by using consistent strain field. Special steps are introduced to circumvent the requirement of C1coninuity in the original plate formulation and C0 continuity of the present element has been compensated in stiffness matrix calculations. The accuracy of the proposed C0 element is established by comparing the results with those obtained by three dimensional elasticity solutions and other finite element analysis.

Displacement finite element models of various beam theories have been developed usingtraditional finite element interpolations (i.e., Hermite cubic or equi-spaced Lagrange functions).Various finite element models of beams differ from each other in the choice of the interpolation functions used for the transverse deflection w, total rotation φ and/or shear strain γxz, or in the integral form used (e.g., weak form or least-squares) to develop the finite element model. The present study is concerned with the development of alternative beam finite elements using hpspectral nodal expansions to eliminate shear and membrane locking. Both linear and non-linear analysis are carried out using both displacement and mixed finite element models of the beam theories studied. Results obtained are compared with both analytical (series) solutions and nonlinear finite element solutions from literature, and excellent agreement is found for all cases.