Sharif Digital Repository

Micro-rotating disks are extensively used in micro-electromechanical systems such as micro-gyroscopes and micro-rotors. Because of the sensitivity of these elements, enough knowledge about the mechanical behavior of these structures is an essential matter for designers and fabricators. The small-scale effects on the in-plane free vibration of such micro-disks present an important aspect of the mechanical behavior of these elements. The small-scale effects on the in-plane free vibration of these micro-disks are investigated in this study using the modified couple stress theory. By using the Hamilton principle, the partial differential equations governing the coupled radial and tangential... 

Gradient reproducing kernel particle method (GRKPM) is a meshless technique which incorporates the first gradients of the function into the reproducing equation of RKPM. Therefore, in two-dimensional space GRKPM introduces three types of shape functions rather than one. The robustness of GRKPM's shape functions is established by reconstruction of a third-order polynomial. To enforce the essential boundary conditions (EBCs), GRKPM's shape functions are modified by transformation technique. By utilizing the modified shape functions, the weak form of the nonlinear evolutionary Buckley-Leverett (BL) equation is discretized in space, rendering a system of nonlinear ordinary differential equations... 

A new meshless method called gradient reproducing kernel particle method (GRKPM) is proposed for numerical solutions of one-dimensional Burgers' equation with various values of viscosity and different initial and boundary conditions. Discretization is first done in the space via GRKPM, and subsequently, the reduced system of nonlinear ordinary differential equations is discretized in time by the Gear's method. Comparison with the exact solutions, which are only available for restricted initial conditions and values of viscosity, approves the efficacy of the proposed method. For challenging cases involving small viscosities, comparison with the results obtained using other numerical schemes... 

Stability has been one of the major issues of time-domain numerical methods used for solving Maxwell equations. This problem takes a more severe form when additional algorithms are introduced to the computation domain (e.g. Absorbing Boundary Conditions-ABCs). There are a number of methods for investigating the stability of a simulation. In this article the problem of stability of ABCs, has been tackled through a control system's state-space point of view. Thus, occurrence of instability in a simulation can be predicted. © 2007 IEEE  

The scaled boundary finite element method (SBFEM) is known for its inherent ability to simulate unbounded domains and singular fields, and its flexibility in the meshing procedure. Keeping the analytical form of the field variables along one coordinate intact, it transforms the governing partial differential equations of the problem into a system of one-dimensional (initial–)boundary value problems. However, closed-form solution of the said system is not available for most cases (e.g. transient heat transfer, acoustics, ultrasonics, etc.) since the system cannot be diagonalized in general. This paper aims to establish a numerical tool within the context of the shooting technique to evaluate... 

The analytical treatment of an energetically consistent annular crack in a piezoelectric solid subjected to remote opening electromechanical loading is addressed. Potential functions and Hankel transform in combination with a robust technique are employed to reduce the solution of the mixed boundary value problem into a Fredholm integral equation of the second kind. The limiting case of a penny-shaped crack in a piezoelectric medium with energetically consistent boundary conditions over the crack faces is extracted for the first time. The electrical discharge phenomenon within the crack gap is modeled utilizing a non-linear constitutive law and the effects of the breakdown field on the... 

This paper presents a mathematical model for prediction of temperature history, final microstructures, and transformation kinetics in steel rods subjected to non-uniform cooling conditions. To achieve this goal, a mathematical model based on two-dimensional finite element method is developed to solve the governing heat conduction equation with non-uniform boundary conditions. The additivity rule is coupled with the finite element analysis to assess the kinetics of austenite decomposition during continuous cooling. The effect of decarburization during heating stage is also considered in the model employing Fick's second equation. To verify the predictions, time-temperature histories during... 

An exact solution is presented for the nonlinear cylindrical bending and postbuckling of shear deformable functionally graded plates in this paper. A simple power law function and the Mori-Tanaka scheme are used to model the through-the-thickness continuous gradual variation of the material properties. The von Karman nonlinear strains are used and then the nonlinear equilibrium equations and the relevant boundary conditions are obtained using Hamilton's principle. The Navier equations are reduced to a linear ordinary differential equation for transverse deflection with nonlinear boundary conditions, which can be solved by exact methods. Finally, by solving some numeral examples for simply... 

The governing equations of the first-order shear deformation plate theory for FG circular plates are reformulated into those describing the interior and edge-zone problems. Analytical solutions are obtained for axisymmetric and asymmetric behavior of functionally graded circular plates with various clamped and simply-supported boundary conditions under mechanical and thermal loadings. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results, which are in closed form and suitable for design purposes, are verified with known results in the literature. It is shown that there are two... 

Passive control of vibration of beams subjected to moving loads is studied in which, an optimal tuned mass damper (TMD) system is utilized to suppress the undesirable beam vibration. Timoshenko beam theory is applied to the beam model having three types of boundary conditions, namely, hinged-hinged, hinged-clamped, and the clamped-clamped ends, and the governing equations of motion are solved using the Galerkin method. For every set of boundary conditions, a minimax problem is solved using the sequential quadratic programming method and the optimum values of the frequency and damping ratios for the TMD system are obtained. To show the effectiveness of the designed TMD system, simulations of... 

We have used a hierarchical multiscale modeling scheme for the analysis of cortical bone considering it as a nanocomposite. This scheme consists of definition of two boundary value problems, one for macroscale, and another for microscale. The coupling between these scales is done by using the homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. Using the described scheme, we have studied elastic properties of cortical bone considering its nanoscale microstructural constituents with various mineral volume fractions. Since the microstructure of bone... 

In this paper, the truly Meshless Local Petrov-Galerkin (MLPG) method is extended for computation of steady incompressible flows, governed by the Navier-Stokes equations (NSE), in vorticity-stream function formulation. The present method is a truly meshless method based on only a number of randomly located nodes. The formulation is based on two equations including stream function Poisson equation and vorticity advection-dispersion-reaction equation (ADRE). The meshless method is based on a local weighted residual method with the Heaviside step function and quartic spline as the test functions respectively over a local subdomain. Radial basis functions (RBF) interpolation is employed in shape...