Sharif Digital Repository

Optical tweezers provide an accurate measurement technique for evaluating mechanical properties of the living cells and many experimental studies have been done to understand the behavior of cells due to external forces. Numerical studies such as finite element methods have been used in order to simulate mechanical behavior of the Red Blood Cells (RBCs). Recent studies have shown that the particle methods are useful tools to simulate the mechanical behavior of living cells. Since in microscopic scales, using discrete models are preferred than continuum methods, a particle-based method is used to simulate the deformation of RBC which is stretched by optical tweezers. The cytoplasm of RBC is... 

Design and application of superelements in efficient prediction of the structural behavior in a short time has been one of the research interests in the last decade. Superelements are those elements which are capable of producing the same accurate result instead of several combined simple elements. In this paper a new 16-node cylindrical superelement is presented. Static and modal analyses of laminated hollow cylinders subjected to various kinds of loadings and boundary conditions are performed using this element. Some numerical examples are given to illustrate and validate the developed method. The accuracy of the results is evident from comparison of the findings with exact solution method... 

In recent years, development of the superelements has significantly influenced the analysis of structural dynamics. One of the common implementation of this element has been in the analysis of plates and shells. In this paper, application of superelements in the vibration analysis of orthotropic rectangular plates with different boundary conditions is considered, in which bending and in-plane displacements are also included. Results of this study indicate that there is a good agreement between single superelement and 625 elements using conventional methods © 2002 Published by Elsevier Science B.V  

In this work, the authors experimentally show Dirac Leaky Wave Antennas (DLWAs) at upper microwave frequencies. For the first time, DLWAs are implemented using simple Parallel plate waveguide (PPW) technology, while yielding desirable radiation features and continuous beam scanning through broadside, as well as extremely low profile, with significant ease of fabrication, making them well suited for Ku band applications such as satellite communication, radar and emerging fifth-generation (5G). A planar Dirac photonic crystal in PPW is shown with a closed bandgap and linear dispersion around broadside. In this work, 1D and 2D PPDLWAs are designed that provide scannable fan and pencil beams,... 

The implementation of new techniques and design of new elements have been an important issues among finite element researchers. In this regard, a designed super element has been applied to analyze a series of dynamic problems. Findings indicate that in large structure analysis the same results as the conventional method can be obtained when applying a few super elements. The time required for dynamic analysis using a super element is significantly smaller than the regular finite element. In this paper, the forced vibration of laminated composite rectangular plates is analyzed. The dynamic response of the plate, using a four-super element, is obtained. In-plane deformation, as well as bending... 

Application of super-finite element method for eccentrically stiffened laminated plates in free vibration was studied. The super element method offers a relatively simple and efficient means of predicting the natural frequencies with shorter runtime. The results obtained from the extensive numerical evaluation show that the super-element method has an acceptable level of accuracy for stiffened laminated composite plates with a coarse mesh  

The classical continuum theory not only underestimates the stiffness of microscale structures such as microbeams but is also unable to capture the size dependency, a phenomenon observed in these structures. Hence, the non-classical continuum theories such as the strain gradient elasticity have been developed. In this paper, a Timoshenko beam finite element is developed based on the strain gradient theory and employed to evaluate the mechanical behavior of microbeams used in microelectromechanical systems. The new beam element is a comprehensive beam element that recovers the formulations of strain gradient Euler–Bernoulli beam element, modified couple stress (another non-classical theory)... 

In this paper, a size-dependent non-classical yield criterion is introduced on the basis of the modified couple stress theory in order to capture the size-dependency of the micro-scale structure yielding loads where the attempts of the classical yield criteria such as the von-Mises have been in vain. In order to develop the new yield criterion, the deviatoric part of the micro-scale structure strain energy density, including both classical and non-classical parts, is equated to the deviatoric strain energy density of a macro-size tensile-test sample at the yielding point. For bending of microbeams and torsion of microbars, the size-dependent yielding moments have been determined based on the... 

Since the classical continuum theory is neither able to evaluate the accurate stiffness nor able to justify the size-dependency of micro-scale structures, the non-classical continuum theories such as the modified couple stress theory have been developed. In this paper, a new comprehensive Timoshenko beam element has been developed on the basis of the modified couple stress theory. The shape functions of the new element are derived by solving the governing equations of modified couple stress Timoshenko beams. Subsequently, the mass and stiffness matrices are developed using energy approach and Hamilton's principle. The formulations of the modified couple stress Euler-Bernoulli beam element... 

In this article effects of sleepers defect on rail vehicle vibration have been investigated. Two parallel rails of the track have been modeled as Euler-Bernoulli beams on elastic points as rail pads. Also sleepers have been modeled as visco-elastic Euler-Bernoulli beams. It is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. The wheelset has 5 DOF which are longitudinal, vertical and lateral movements plus roll and axial rotations. To determine normal contact force between wheel and rail, relative position of wheel and rail has been determined at each instant. Using the coordinate of each wheel points in rail coordinate system, the penetration of... 

The classical continuum theory is neither able to accurately model the mechanical behavior of micro/nano-scale structures nor capable of justifying the size-dependent behavior observed in these structures; so the non-classical continuum theories such as the strain gradient theory have been emerged and developed. In order to enable the finite element method (FEM) to more accurately deal with the problems in micro/nano-scale structures, a size-dependent Euler-Bernoulli beam element is developed based on the strain gradient theory. Compared to the classical Euler-Bernoulli beam element, the nodal displacement vector of the new Euler-Bernoulli beam element has an additional component, i.e. the... 

This paper is devoted to investigate the nonlinear behaviors of a V-shaped microcantilever of an atomic force microscope (AFM) operating in its two major modes: amplitude modulation and frequency modulation. The nonlinear behavior of the AFM is due to the nonlinear nature of the AFM tip-sample interaction caused by the Van der Waals attraction/repulsion force. Considering the V-shaped microcantilever as a flexible continuous system, the resonant frequencies, mode shapes, governing nonlinear partial and ordinary differential equations (PDE and ODE) of motion, boundary conditions, frequency and time responses, potential function and phase-plane of the system are obtained analytically. The... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

In this study, using analytical method, the torsional resonant frequency and torsional sensitivity of the first four modes of an AFM cantilever with sidewall probe including a horizontal cantilever and a vertical extension is analyzed and a closed form for torsional sensitivity of the probe is derived. In addition, the effect of relative parameters such as ratio of vertical extension length to horizontal cantilever length is investigated. According to this study, the results show that as contact stiffness increases, the resonant frequencies of all vibration modes increases until they reach constant values at very high values of contact stiffness. It is also can be found that low-order modes... 

In this study, using analytical method, the torsional resonant frequency and torsional sensitivity of the first four modes of an AFM cantilever with sidewall probe including a horizontal cantilever and a vertical extension is analyzed and a closed form for torsional sensitivity of the probe is derived. In addition, the effect of relative parameters such as ratio of vertical extension length to horizontal cantilever length is investigated. According to this study, the results show that as contact stiffness increases, the resonant frequencies of all vibration modes increases until they reach constant values at very high values of contact stiffness. It is also can be found that low-order modes... 

Structures of tapered geometry are customarily used in a variety of applications. The analysis of such structures is usually made through finite element method using traditional beam, shell or brick elements. In this paper, a new tapered superelement is presented that lends itself to modeling revolving geometries under lateral, axial and torsional loads. The presented tapered superelement has 16 nodes. The performance of this element under static and dynamic loading and in rotating condition is examined. It is shown that this element yields accurate results with higher computational efficiency compared to conventional elements. Furthermore, it is verified that a single tapered superelement... 

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... 

A finite element formulation is derived for the structural analysis of functionally graded hollow cylinders. The power-law distribution model is used for the composition of the constituent material in the thickness direction. According to property variation in FG cylinders, it is difficult to analyze them using the conventional element formulation. In order to facilitate the process of modeling and analyzing the FG cylinders, the finite element formulation is based on a newly designed cylindrical element. The new cylindrical element allows for property variations along the thickness, which results in considerable reduction of the required elements and eliminates the need to mesh the cross... 

This paper uses Hes Homotopy Perturbation Method (HPM) to analyze the nonlinear free vibrational behavior of clamped-clamped and clamped-free microbeams considering the effects of rotary inertia and shear deformation. Galerkins projection method is used to reduce the governing nonlinear partial differential equation. to a nonlinear ordinary differential equation. HPM is used to find analytic expressions for nonlinear natural frequencies of the pre-stretched microbeam. A parametric study investigated the effects of design parameters such as applied axial loads and slenderness ratio. The effect of rotary inertia and shear deformation on the nonlinear natural frequency was investigated. For... 

In this study, the homotopy analysis method (HAM) is used to obtain an approximate analytical solution for geometrically non-linear vibrations of thin laminated composite plates resting on non-linear elastic foundations. Geometric non-linearity is considered using von Karman's straindisplacement relations. Then, the effects of the initial deflection, ply properties, aspect ratio of the plate and foundation parameters on the non-linear free vibration is studied. Comparison between the obtained results and those available in the literature demonstrates the potential of HAM for the analysis of such vibration problems, whose governing differential equations include the quadratic and cubic...