Sharif Digital Repository

In this study, an efficient frequency-independent and error-controllable Filon-type solution of highly oscillatory physical optics (PO) integrals on the quadratic surfaces is presented. In this method first, PO surface integral is decomposed into some analytically solvable integrals and one highly oscillatory integral (HOI) which must be solved numerically. Then, by demodulating complementary error function, the integrand of this HOI is decomposed into an oscillatory part and a slowly varying part (demodulated part). The demodulated part can be easily approximated by various types of basis functions, especially in high frequencies. Therefore, after approximating the demodulated part using... 

The current paper focuses on the non-linear torsional vibration of a one-stage transmission gear system. Four different methods have been applied for solution of the equation of motion; the discretization method, the perturbation method, the Ritz method, and the stepwise time integration of the equation of motion. The time and frequency results from these analyses have been compared with each other, as well as those reported in literatures. Although all of these methods are accurate and computationally effective for finding the main spectral contribution, however, only the discretization method and the step-wise time-integration model are able to identify the other frequency components. ©... 

The nonlinear aeroelastic behavior of a three-dimensional general laminated composite plate at high supersonic Mach numbers is investigated using von Karman's large deflection plate theory and quasisteady aerodynamic theory. Galerkin's method is used to reduce the governing equations to a system of nonlinear ordinary differential equations in time, which are then solved by a direct numerical integration method. Nonlinear flutter results are presented with the effects of in-plane force, static pressure differential, fiber orientation and aerodynamic damping  

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed... 

The most suitable and widely used numerical integration method for boundary integrals in the BEM method is Gauss-Legendre integration. But, this integration method is not appropriate for singular and nearly singular integrations in BEM. In this study, some criteria are introduced for recognizing nearly singular integrals in the integral form of the Laplace equation. At the first stage, a criterion is obtained for the constant element and, at the later stages, higher order elements are investigated. In the present research, the Romberg integration method is used for nearly singular integrals. The results of this numerical method have good agreement with analytical integration. The singular... 

The density jump on an inclined surface is analyzed using an integral method by applying mass and momentum conservation equations. The jump occurs in a two-layered fluid flow in which the upper layer is stagnant and very deep. A relation is derived, which gives the conjugate depth ratio as a function of inlet densimetric Froude number, inlet concentration ratio, bed slope and entrainment. A set of experiments are performed to verify the relation. The theory and the measurements are in good agreement. The analysis reveals that increasing the surface inclination results in a decrease in the conjugate depth ratio. This analysis also shows that the densimetric Froude number just after the jump... 

In this paper, the fully coupled rolling contact problem of a graded coating/substrate system under the action of a rigid cylinder is investigated. Using the singular integral equation approach, the governing equations of the rolling contact problem are constructed for all possible stick/slip regimes. Applying the Gauss-Chebyshev numerical integration method, the governing equations are converted to systems of algebraic equations. A new numerical algorithm is proposed to solve these systems of equations. Both the coupled and the uncoupled solutions to the problem are found through an implemented iterative procedure. In Part I of this paper, the analytical formulation of the rolling contact... 

Convection heat transfer below a horizontal, hot, and isothermal strip of infinite length and width of 2L embedded in fluids with different Prandtl number (Pr) and Nusselt number (Nu) is analyzed with the aid of integral method. A new concept is utilized to determine the boundary layer thickness at the strip's edge, which is based on matching the flow rate of the boundary layer below the strip at its edge and the flow rate of the plume, which forms after the heated fluid detaches from the strip's edge. In addition to these novelties, a numerical model is developed to verify the analytical framework, and an excellent agreement is observed between the analytical and numerical models  

In this paper the Contour Integral (CI) method is applied to the design and analysis of substrate integrated waveguide (SIW) filters. This method is used for planar structures and is based upon the discretization of the boundary of the structure and needs less memory than full wave methods. For decreasing the computation time, circular vias replaced by square ones. A four pole Chebyshev X band dual inductive post substrate integrated waveguide filter is designed using this technique and the results are compared with measurements and simulation software Ansoft HFSS. Good agreement is seen between the results  

Composite structures encounter different types of imperfections and defects during the installation, working environment, and fabrication process. In the present research, a 3D-poroflexibility theory has been presented to study the bending responses of the functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) axisymmetric circular/annular sector plates on the elastic substrate. For modeling elastic substrate, horizontal friction force and the elastic foundation with five elastic parameters have been formulated. For obtaining the exact displacement and stress/strain responses of the current structure, a discrete singular convolution integration method (DSC-IM) has been... 

The boundary layer integral method is used to investigate the development of the turbulent swirling flow at the entrance region of a conical nozzle. The governing equations in the spherical coordinate system are simplified with the boundary layer assumptions and integrated through the boundary layer. The resulting sets of differential equations are then solved by the fourth-order Adams predictor-corrector method. The free vortex and uniform velocity profiles are applied for the tangential and axial velocities at the inlet region, respectively. Due to the lack of experimental data for swirling flows in converging nozzles, the developed model is validated against the numerical simulations. The... 

In this work a new method for analyzing nanostructured materials has been proposed to accelerate the simulations for solid crystalline materials. The proposed Structural Approximation Method (SAM) is based on Molecular Dynamics (MD) and the accuracy of the results can also be improved in a systematic manner by sacrificing the simulation speed. In this method a virtual material is used instead of the real one, which has less number of atoms and therefore fewer degrees of freedom, compared to the real material. The number of differential equations that must be integrated in order to specify the state of the system will decrease significantly, and the simulation speed increases. To generalize... 

This paper develops a two dimensional Green element simulator based on a "compatibility-equation" algorithm for simulation of counter-current spontaneous imbibition (COUCSI) process. The Green element method is a novel computational approach based on the boundary integral theory, which is regarded as a hybrid combination of both boundary and finite element methods. The superiority of the Green element method in modeling of two phase water/oil flow is at the core of this paper. The developed simulator within the context of this proposition is explored to predict the oil recovery from a one dimensional single matrix block. The results are then compared with the experimental data, and they... 

Employing a biharmonic boundary integral method with linear elements, coarsening dynamics of nanodroplets on topographical step heterogeneity is investigated. It is shown that the step height and droplet configuration have an influential effect on the dynamics. Increasing the step height slows down the process while locating the droplets close to the step boosts the coarsening rate. Considering a slip boundary condition enhances the dynamics and reveals a transition in the droplet migration direction. Our results reveal that increasing the surface wettability weakens the dynamics. Various types of the disjoining pressure over the step are also considered and their effects on the coarsening... 

This paper proposes a new visco-hyperelastic constitutive law for modeling the finite-deformation strain rate-dependent behavior of foams as compressible elastomers. The proposed model is based on a phenomenological Zener model, which consists of a hyperelastic equilibrium spring and a Maxwell element parallel to it. The hyperelastic equilibrium spring describes the steady state response. The Maxwell element, which captures the rate-dependency behavior, consists of a nonlinear viscous damper connected in series to a hyperelastic intermediate spring. The nonlinear damper controls the rate-dependency of the Maxwell element. Some strain energy potential functions are proposed for the two...