Sharif Digital Repository

In this article, the homotopy analysis method has been applied to solve a coupled nonlinear diffusion-reaction equations. The validity of this method has been successful by applying it for these nonlinear equations. The results obtained by this method have a good agreement with one obtained by other methods. This work illustrates the validity of the homotopy analysis method for the nonlinear differential equations. The basic ideas of this approach can be widely employed to solve other strongly nonlinear problems. © 2008 Springer Science+Business Media B.V  

An inverse finite element method (IFEM) has been developed for estimation of the blank size and prediction of the strain distribution in sheet metal forming. In the inverse method the nodal coordinates in the final shape are known and their corresponding positions on the initial blank should be determined. The developed method deals with logarithmic large strains of membrane triangular elements, virtual work principle and a new approach for friction modeling. This method leads to a system of nonlinear equations which is highly sensitive to the initial guess. In order to avoid the converging problems, especially in the quasi-vertical walls, an appropriate initial guess is introduced. The... 

This paper is concerned with the study of the oscillatory behavior of an electrostatically actuated microcantilever gyroscope with a proof mass attached to its free end. In mathematical modeling, the effects of different nonlinearities such as electrostatic forces, fringing field, inertial terms and geometric nonlinearities are considered. The microgyroscope is subjected to bending oscillations around the static deflection coupled with base rotation. The primary oscillation is generated in drive direction of the microgyroscope by a pair of DC and AC voltages on the tip mass. The secondary oscillation occurring in the sense direction is induced by the Coriolis coupling caused by the input... 

Vibratory micromachined gyroscopes use suspending mechanical parts to measure rotation. They have no gyratory component that require bearings, and for this reason they can be easily miniaturized and batch production using micromachining methods. They operate based on the energy interchange between two modes of structural vibration. The objective of this paper is to study the oscillatory behavior of an electrostatically actuated vibrating microcantilever gyroscope with proof mass at its end. In the modelling, the effects of different nonlinearities, fringing field and base rotation are considered. The microgyroscope is subjected to coupled bending oscillations around the static deflection... 

In this paper, an extended finite element method is presented for simulation of interaction between hydraulic fracturing and natural fractures in saturated porous media. The well-known u−p formulation is employed in order to obtain the fully coupled set of governing equations. Natural faults are modeled for both opening and closure modes where the fluid inflow and contact conditions are considered at the interface, respectively. The Darcy law is employed in conjunction with an aperture dependent permeability for the fracture channel to describe the interfacial inflow. The contact constraints of both the solid and fluid phases are imposed using the Penalty method. The Heaviside and modified...