Sharif Digital Repository

In this paper an analytical solution for size-dependent response of cantilever micro-beams is presented. Using the modified couple stress theory, the small scale effects are accounted for. Employing the Modified Variational Iteration Method, efficient and accurate analytical expressions for the deflection of the micro-beam are presented. Very good agreement is observed between the present work results and available experimental data. This study may be helpful to characterize the size-dependent mechanical properties of MEMS. Consequently, the proposed analytical solution can be used as an efficient tool for studying the effects of the material or geometrical parameters on small scale devices... 

This is a theoretical study that extends a classical method of treating the convection heat transfer in complex geometries to gaseous slip flow forced convection in microchannels with H1 thermal boundary condition. Through this line, the momentum and energy equations in cylindrical coordinates are made dimensionless. Afterward, solutions are presented that exactly satisfy the dimensionless differential equations along with the symmetry condition and finiteness of the flow parameter at the origin. The first-order slip boundary conditions are then applied to the solution utilizing the least squares matching method. Though the method is general enough to be applied to almost any arbitrary cross... 

In this paper, employing the limit analysis theorem, critical loading on functionally graded (FG) circular plate with simply supported boundary conditions and subjected to an arbitrary rotationally symmetric loading is determined. The material behavior follows a rigid-perfectly plastic model and yielding obeys the von-Mises criterion. In the homogeneous case, the highly nonlinear ordinary differential equation governing the problem is analytically solved using a variational iteration method. In other cases, numerical results are reported. Finally, the results are compared with those of the FG plate with Tresca yield criterion and also in the homogeneous case with those of employing the... 

In many engineering applications, shape memory polymers (SMPs) usually undergo arbitrary thermomechanical loadings at finite deformation. Thus, development of 3D constitutive models for SMPs within the finite deformation regime has attracted a great deal of interest. In this paper, based on the classical framework of thermodynamics of irreversible processes, employing the logarithmic (or Hencky) strain as a more physical measure of strain, a 3D large-strain macromechanical model is presented. In the constitutive model development, we adopt a multiplicative decomposition of the deformation gradient into elastic and stored parts. In addition, employing the averaging scheme, the logarithmic... 

The purpose of this paper is to present efficient and accurate analytical expressions for deflection of a shape memory polymer (SMP) beam employing Euler-Bernoulli beam theory in a thermomechanical SMP cycle. Material behavior is considered using a recently 3D thermodynamically consistent constitutive model available in literature. In different steps of an SMP thermomechanical cycle, closed form expressions for internal variables variations, stresses and beam curvature distribution are presented. We show that during the cooling process, stored strains evolve to fix the temporary shape and then during the heating process they relax to recover the permanent shape. Effects of applying external... 

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration analysis of single and double tapered beams on elastic foundation. Geometric nonlinearity is considered using the condition of inextensibility of neutral axis. Moreover, the elastic foundation consists of a linear and cubic nonlinear parts together with a shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the second-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the nonlinear... 

An analytical study using Variational Iteration Method (VIM) is carried out in order to investigate the vibrations of electro-statically actuated double-clamped and simply-supported microbeams. Effects of applied voltage and residual axial load on the nonlinear natural frequency and deflection of the microbeams are studied. It shows that pre-compression in microbeams increases the amplitude of deflections for a specific applied voltage. Also, an increase in pre-tension motivates the microbeam to show more nonlinear behavior in an applied voltage. Predicted results are compared with the experimental data available in the literature and also with numerical results which shows a good agreement.... 

Shape memory polymers commonly experience both finite deformations and arbitrary thermomechanical loading conditions in engineering applications. This motivates the development of three-dimensional constitutive models within the finite deformation regime. In the present study, based on the principles of continuum thermodynamics with internal variables, a three-dimensional finite deformation phenomenological constitutive model is proposed taking its basis from the recent model in the small strain regime proposed by Baghani et al. (2012). In the constitutive model derivation, a multiplicative decomposition of the deformation gradient into elastic and inelastic stored parts (in each phase) is... 

In this paper, an analytical solution for the nonlinear free vibration of a conservative oscillator is presented. The nonlinear governing equation is solved by employing the Variational Iteration Method (VIM). This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a function. Obtained results reveal that the proposed method is very effective, simple and exact. In the present investigation, the results of this method are compared with those of the Homotopy Analysis Method (HAM), as well as those predicted by the Runge-Kutta method. The excellent accuracy of the obtained results is demonstrated by comparing them with available analytical... 

In this paper, the responses of shape memory polymer (SMP) helical springs under axial force are studied both analytically and numerically. In the analytical solution, we first derive the response of a cylindrical tube under torsional loadings. This solution can be used for helical springs in which both the curvature and pitch effects are negligible. This is the case for helical springs with large ratios of the mean coil radius to the cross sectional radius (spring index) and also small pitch angles. Making use of this solution simplifies the analysis of the helical springs to that of the torsion of a straight bar with circular cross section. The 3D phenomenological constitutive model... 

Gold and copper thin films are widely used in microelectromechanical system (MEMS) and nanoelectromechanical system (NEMS) devices. Nanoindentation has been developed in mechanical characterization of thin films in recent years. Several researchers have examined the effect of surface roughness on nanoindentation results. It is proved that the surface roughness has great importance in nanoindentation of thin films. In this paper, the surface topography of thin films is simulated using the extracted data from the atomic force microscopy (AFM) images. Nanoindentation on a rough surface is simulated using a three-dimensional finite-element model. The results are compared with the results of... 

In this article, satisfying the second law of thermodynamics, we present a 3D constitutive model for shape memory polymers. The model is based on an additive decomposition of the strain into four parts. Also, evolution laws for internal variables during both cooling and heating processes are proposed. Since temperature has considerable effect on the shape memory polymer behavior, for simulation of a shape memory polymer-based structure, it is required to perform a heat-transfer analysis. Commonly, an experimentally observed temperature rate-dependent behavior of shape memory polymers is justified by a rate-dependent glassy temperature, but using the heat-transfer analysis, it is shown that... 

The ever increasing applications of shape memory polymers have motivated the development of appropriate constitutive models for these materials. In this work, we present a 3 D constitutive model for shape memory polymers under time-dependent multiaxial thermomechanical loadings in the small strain regime. The derivation is based on an additive decomposition of the strain into six parts and satisfying the second law of thermodynamics in Clausius-Duhem inequality form. In the constitutive model, the evolution laws for internal variables are derived during both cooling and heating thermomechanical loadings. The viscous effects are also fully accounted for in the proposed model. Further, we... 

The purpose of this paper is to present efficient and accurate analytical expressions for large amplitude free vibration and post-buckling analysis of unsymmetrically laminated composite beams on elastic foundation. Geometric nonlinearity is considered using Von Karman's strain-displacement relations. Besides, the elastic foundation has cubic nonlinearity with shearing layer. The nonlinear governing equation is solved by employing the variational iteration method (VIM). This study shows that the third-order approximation of the VIM leads to highly accurate solutions which are valid for a wide range of vibration amplitudes. The effects of different parameters on the ratio of nonlinear to... 

In this paper, employing the definition of an effective configuration in the continuum damage mechanics, mechanical response of a compressible viscoelastic-viscoplastic material is investigated. We present a phenomenological viscoelastic-viscoplastic-viscodamage constitutive model, developed within the framework of irreversible thermodynamics. The formulation is based on the additive decomposition of the total strain into elastic, viscoelastic, and viscoplastic parts in the effective configuration. Thus, the Helmholtz energy is partitioned into elastic, elastic-viscoelastic, and viscoplastic parts. Then, each one is divided into deviatoric and volumetric energies. Considering the... 

In this paper, employing the Hencky strain, viscoelastic-viscoplastic response of self-healing materials is investigated. Considering the irreversible thermodynamics and using the effective configuration in the Continuum Damage-Healing Mechanics (CDHM), a phenomenological finite strain viscoelastic-viscoplastic constitutive model is presented. Considering finite viscoelastic and viscoplastic deformations, total deformation gradient is multiplicatively decomposed into viscoelastic and viscoplastic parts. Due to mathematical advantages and physical meaning of Hencky strain, this measure of strain is employed in the constitutive model development. In this regard, defining the damage and healing...