Sharif Digital Repository

In this study, effects of geometric factors and material properties are investigated on stress behavior of circular rotating disk with constant rotation in various industrial mechanisms using equilibrium equations, geometric relations and stress functions. In this way, research on a thin uniform and homogeneous circular disk under constant rotation is considered. The rotating motion produces centrifugal acceleration on each element of the rotating disk, and this rotating motion becomes the source of external loading for the mentioned problem. Additional exterior loadings are not assumed in this problem. It is comfortable to handle the centrifugal force loading by relating it to a body force... 

This paper presents analytical soltions for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. First the energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. These equations are then solved using Homotopy Perturbation Method (HPM) for the especial case of α = 0 where α is a small nondimensional geometrical parameter defining the starting point of the underneath electrodes. Then straight forward perturbation method is applied for finding the pull-in angle and pull-in displacement of the... 

In this work an analytical solution is presented for a viscoelastic micro-beam based on the modified couple stress theory which is a non-classical theory in continuum mechanics. The modified couple stress theory has the ability to consider small size effects in micro-structures. It is strongly emphasized that without considering these effects in such structures the solution will be wrong and not suitable for designing systems in micro-scales. In this study correspondence principle is used for deriving constitutive equations for viscoelastic material based on the modified couple stress theory. Governing equilibrium equations are obtained by considering an element of micro-beam. Closedform... 

In this paper, the effects of van der Waals and Casimir forces on the static deflection and pull-in instability of a micro/nano cantilever gyroscope with proof mass at its end are investigated. The micro/nano gyroscope is subjected to coupled bending motions which are related by base rotation and nonlinearities due to the geometry and the inertial terms. It is actuated and detected by capacitance plates which are placed on the proof mass. The extended Hamilton principle is used to find the equations governing the static behavior of the clamp-free micro/nano gyroscopes under electrostatic, Casimir and van der Waals forces. The equations of static motion are discritized by Galerkin's... 

The current paper presents a two degree of freedom model for the problem of nano/micromirrors under the effect of vdW force. Energy method, the principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the nano/micromirror. Then using the implicit function theorem, a coupled bending-torsion model is presented for the pull-in characteristics of nano/micromirrors under vdW force and the concept of instability mode is introduced. It is observed that with increasing the ratio of the bending stiffness to the torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. It is shown that... 

In this research, the static behavior of torsional nano-/micro-actuators under van der Waals (vdW) force is studied. First, the equilibrium equation governing the static behavior of torsional nano-/micro-actuators under vdW force is obtained. Then the energy method is utilized to investigate the statical stability of nano-/micro-actuator equilibrium points and a useful equation is suggested for the successful and stable design of nano-/micro-actuators under vdW force. Then, the equilibrium angle of nano-/micro-actuators is calculated both numerically and analytically using the homotopy perturbation method (HPM). It is observed that, with increasing instability number, defined in this paper,... 

In the current paper, analytical solutions are presented for the nonlinear problem of electrostatically actuated torsional micromirrors considering the bending of the torsional beams. Energy method is used for finding the equilibrium equations. Then the explicit function theorem is utilized for finding the equations governing the instability mode of the mirror. The presented results show that neglecting the bending effect in electrostatic torsion micro actuators can cause to several hundred percent of overestimation of the stability limits of the device. In order to study the voltage-angle and voltage-displacement behavior of the micromirror, equilibrium equations are solved using HPM.... 

The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flügge's shell theory and the stress-stain equations of Eringen's nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the... 

In this paper, a refined finite element method (FEM) based on the Carrera unified formulation (CUF) is extended for stress analysis of rotors and rotating disks with variable thickness. The variational form of the 3D equilibrium equations is obtained using the principle of minimum potential energy and solved by this method. Employing the 1D CUF, a rotor is assumed to be a beam along its axis. In this case, the geometry of the rotor can be discretized into a finite number of 1D beam elements along its axis, while the Lagrange polynomial expansions may be employed to approximate the displacement field over the cross section of the beam. Therefore, the FEM matrices and vectors can be written in... 

The underground and buried oil and gas pipelines are continuously in contact with earthen soils on the outer surface and compressible fluids on the inner surface. Most these earthen soils can be appropriately represented by a model named Pasternak. Similarly, undersea oil and gas pipelines and tubes of heat exchangers remain in contact with fluids on both sides and also rockets and missiles filled with solid and liquid fuels and shallow shells supported on soft and light filaments in space vehicles, boilers and storage tanks on floor grid work in ships can also be considered as thin circular cylindrical shells on a Pasternak foundation. The basic aim of the presented study is investigation... 

In this paper, a computational modeling tool is developed for fully coupled multiphase flow in deformable heterogeneous porous medium that consists of complex and non-uniform micro-structures using the dual continuum scales based on the computational homogenization approach. The first-order homogenization technique is employed to perform the multi-scale analysis. The governing equations of two-phase flow of immiscible fluids, including an equilibrium equation and two mass continuity equations, are considered based on the appropriate main variables. According to the well-known Hill–Mandel principle of macro-homogeneity, the proper energy types are defined instead of conventional stress power... 

In this paper, the nonlinear three-dimensional (3D) stress analysis of shell structures in buckling and snapping problems is presented. The exact geometry or geometrically exact (GeX) hybrid-mixed four-node solid-shell element is developed using a sampling surfaces (SaS) method. The SaS formulation is based on the choice of N SaS parallel to the middle surface to introduce the displacements of these surfaces as basic shell unknowns. The SaS are located at the Chebyshev polynomial nodes (roots of the Chebyshev polynomial of degree N), that is, the outer surfaces are not included into a set of SaS. Such choice of unknowns with the consequent use of Lagrange polynomials of degree N–1 in the... 

In this paper, a new analytical approach is proposed for free vibration and buckling analysis of a rectangular Mindlin plate resting on the Winkler–Pasternak foundation of varying stiffness. According to Mindlin theory, there are three independent governing differential equations. Thus, three Fourier series expansions along with auxiliary polynomial functions are employed to represent the plate's deflection and rotation angle functions. The process of making a set of equations is then completed satisfying the corresponding equilibrium equations and boundary conditions. The proposed method incorporates general elastic supports for all plate's edges, and subsequently can deal with all possible... 

In this paper, static behavior of nano/microm1irrors under Casimir force is studied. At the first, the equilibrium equation governing the statical behavior of nano/micromirrors is obtained. Then energy method is employed to investigate statical stability of nano/micromirrors equilibrium points and a useful equation is suggested for successful and stable design of nano/micromirrors under Casimir force. Then, equilibrium angle of nano/micromirrors is calculated both numerically and analytically using the homotopy perturbation method (HPM). It is observed that with increasing the instability number defined in the paper, the rotation angle of the mirror is increased and suddenly, pull-in occurs.... 

The current paper presents a two degree of freedom model for the problem of micromirrors under capillary force. The principal of minimum potential energy is employed for finding the equilibrium equations governing the deflection and the rotation of the micromirror. Then, using the implicit function theorem, a coupled bending-torsion model is presented for pull-in characteristics of micromirrors under capillary force and the concept of instability mode is introduced. It is observed that with increasing ratio of bending and torsion stiffness, the dominant instability mode changes from bending mode to the torsion mode. In order to verify the accuracy of the coupled model, static behavior of a... 

This paper deals with analytical thermomechanical stress analysis of adhesively bonded composite joints in presence of a structural imperfection in the form of an interfacial void within the adhesive layer based on the full layerwise theory (FLWT). The joints are subjected to mechanical tension, uniform temperature change, or steady-state heat conduction. The proposed adhesive joint is divided into three distinct regions along its length and a large number of mathematical plies through its thickness. Three sets of fully coupled governing equilibrium equations are derived employing the principle of minimum total potential energy. The three-dimensional nonlinear interlaminar stress... 

In this paper a linear continuous theory for bending analysis of beams with an edge crack perpendicular to the neutral plane subject to bending has been developed. The model assumes that the displacement field is a superposition of the classical EulerBernoulli beam's displacement and of a displacement due to the crack. It is assumed that in bending the additional displacement due to crack decreases exponentially with distance from the crack tip. The strain and stress fields have been calculated using this displacement field and the bending equation has been obtained using equilibrium equations. Using a fracture mechanics approach the exponential decay rate has been calculated. There is a... 

In this study, the buckling and postbuckling analysis of FG micro-plates under different kinds of traction on the edges is investigated based on the modified couple stress theory. The static equilibrium equations of an FG rectangular micro-plate as well as the boundary conditions are derived using the principle of minimum total potential energy. The analytical solutions are developed for three case studies including: simply supported micro-plates subjected to uniform transverse load and biaxial tractions, clamped-simply supported micro-plates under uniform transverse load and axial traction, and simply supported micro-plates subjected to shear traction. All plate properties except the length... 

In this work, a novel multi-layer pressure-temperature swing adsorption (PTSA) process was designed for efficient simultaneous water and mercaptans removal from natural gas (NG) to less than 0.1 ppmv and 3 ppmv in a mini liquefied NG unit. The proposed multi-layer PTSA consists of a three-layer fixed bed including activated alumina, molecular sieves 4A and 13X. To gain in-depth insights about the process, a descriptive model considering mass, energy and momentum balances, along with the kinetic and equilibrium equations was developed. After validating the model with the experimental and operational data from the literature, the total energy requirement and long-term operational requirements... 

Governing equilibrium equations of thick-walled spherical vessels made of material following linear strain hardening and subjected to a steady-state radial temperature gradient using elasto-plastic analysis are derived. By considering a maximum plastic radius and using the concept of thermal autofrettage for the strengthening mechanism, the optimum wall thickness of the vessel for a given temperature gradient across the wall thickness is obtained. Finally, in the case of thermal loading on a vessel, the effect of convective heat transfer on the optimum thickness is studied and a general formula for the optimum wall thickness and design graphs for several different cases are presented. © 2008...