Sharif Digital Repository

In the current study, the elastic field in an anisotropic elastic media is determined by implementing a general semi-analytical method. In this specific methodology, the displacement field is computed as a sum of finite functions with unknown coefficients. These aforementioned functions exactly satisfy both the homogeneous and inhomogeneous boundary conditions in the proposed media. It is worth mentioning that the unknown coefficients are determined by implementing the principle of minimum potential energy. The numerical integration is done by employing the Generalized Gaussian Quadrature rule. Furthermore, and with the aid of the calculated unknown coefficients, the displacement fields as... 

The requirement of reliable relative permeability data is more intensified when the miscibility condition approaches. In this work the relative permeability of CO2 and oil has been measured at different miscibility conditions using conventional methods. Fractured dolomite and sandstone core plugs samples were used in the experiments. Due to some errorful assumptions of conventional methods such as immiscible, incompressible displacement, inverse modeling was used for predicting the reliable relative permeability of oil and gas phases at near miscible condition from measured oil production and pressure drop data. The initial guesses of relative permeabilities were provided from conventional... 

A sheet of graphene under magnetic bias attains anisotropic surface conductivity, opening the door for realizing compact devices such as Faraday rotators, isolators and circulators. In this paper, an accurate and analytical method is proposed for a periodic array of graphene ribbons under magnetic bias. The method is based on integral equations governing the induced surface currents on the coplanar array of graphene ribbons. For subwavelength size ribbons subjected to an incident plane wave, the current distribution is derived leading to analytical expressions for the reflection/transmission coefficients. The results obtained are in excellent agreement with full-wave simulations and predict... 

The effect of compressive Residual Stress (RS) on the Stress Intensity Factors (SIFs) of fretting fatigue cracks was studied using semi-analytical methods. The fretting fatigue of a half-plane in contact with a flat rounded pad was taken into consideration, and RS such as those created by shot-peening were added to the model. Studies of several RS profiles were accomplished to consider the effect of changes in RS caused by stress relaxation during service or pretreatment and manufacturing discrepancies regarding parameters. The distribution of dislocations method was applied to the calculation of the SIFs of these cracks and was shown to be capable of dealing with these kinds of problems. It... 

A general three-dimensional semi-analytical solution of piezocomposite media consisting of various domains of distinct electro-mechanical properties is proposed. The interfaces between the domains may be non-planar. The geometry and boundary conditions may be arbitrary, and the applied loading can be in the form of traction, displacement, voltage, or any combination of them. In this approach, the unknown displacement field u1, u2, u3, and the electric potential φ are taken as appropriate functions in each domain, such that the continuity of the displacement field and the electric potential are exactly satisfied at the interfaces. Also, the continuities of traction stresses and normal... 

Elastic stability of shell structures under certain loading conditions is characterized by a dramatically unstable postbuckling behavior. The presence of simultaneous 'competing' buckling modes (corresponding to the same critical buckling load) is understood to be largely responsible for such behavior. In this paper, within the framework of linear bifurcation eigenvalue analysis and Donnell shallow shell theory, the presence of simultaneous buckling modes in axially compressed isotropic cones is determined using the semi-analytical method of Galerkin. The results are presented in the plane of the dimensionless reciprocal meridional and circumferential buckling half wavelengths, and are... 

In this study a 3D robust, systematic, semi-analytical method to characterize electromagnetic scattering from periodic arrays of discrete scatterers is presented. The proposed method is based on the multiple-scattering T-matrix in connection with the Ewald method. The formulation is systematic, quite general, easily traceable, and fast. Its high speed of analysis makes it well suited to design optimizations. The formulation is well developed for obliquely incident plane waves, and can be extended to Gaussian beams by means of suitable plane wave decomposition. For validating the proposed method, an example of a scattering problem is solved, and the resulting scattering spectrum, and the... 

The present research is performed to calculate the natural frequencies, loss factors, and associated mode shapes of a sandwich cylinder with moderately thick functionally graded (FG) face sheets and an electrorheological (ER) fluid core. Each face sheet is assumed to be made of FG materials, and its displacement field is estimated based on the first-order shear deformation theory, like the ER constrained layer. A suitable displacement continuity condition is considered between layers. The ER fluid used in the central middle is analyzed in the pre-yield area and considered electric field dependent. Hamilton's principle is used to acquire the motion equations related to each layer and... 

In this work, a general semi-analytical method for the determination of the elastic fields within an anisotropic homogeneous elastic solid with an inclined edge or interior crack is developed. In this method, the displacement field is represented as a sum of a function and a finite series of functions with unknown coefficients. The functions are constructed in such a way that all the essential homogeneous and inhomogeneous boundary conditions are satisfied exactly and, moreover, the displacement discontinuity across the crack faces as well as the exact singular behaviour of the stress field at the crack-tip are captured. The unknown coefficients are determined by utilizing the principle of... 

A rather new semi-analytical method towards investigating the free vibration analysis of generally laminated composite beam (LCB) with a delamination is presented. For the first time the combined effects of material couplings (bending-tension, bending-twist, and tension-twist couplings) with the effects of shear deformation, rotary inertia and Poisson's effect are taken into account. The semi-analytical solution for the natural frequencies and mode shapes are presented by incorporating the constraint conditions using the method of Lagrange multipliers. To verify the validity and the accuracy of the obtained results, they were compared with the results from other available references. Very... 

A semi-analytical method is presented to calculate the dynamic responses of a rectangular plate due to a moving oscillator. In previous analytical solutions of the moving oscillator problem, the elastic distributed structure has usually been modeled by an elastic beam structure. This restrictive assumption is removed in this study by assuming a general plate as two-dimensional elastic distributed structure. The method can be applied for any arbitrary path on the plate. A combination of the Fourier and Laplace transformation as well as the convolution theorem is used to solve the governing differential equations of the problem. A modified integration technique is then presented to solve the... 

The need for antennas with improved characteristics for communication and radar applications has resulted in an ever-increasing demand for research in the field of high impedance surfaces, which can work as an artificial magnetic conductor. One method in fabrication of these surfaces is formation of a metamaterial by patterning a metallic surface in the shape of space filling curves (e.g. Hilbert or Peanu Curves). In this paper, we present a novel semi-analytical solution to the problem of plasmonic propagation on these surfaces. The method is based on a previously presented Green's function formalism, which has been reported in an earlier paper of ours. We have modified and improved the... 

A semi-analytical method is proposed to solve the equations governing a bi-directionally pumped Raman amplifier through continuous-spectrum radiation. The governing equations are systems of uncountable Nonlinear Ordinary Differential Equation (NODE). By applying the moment method, the uncountable system of NODE is reduced to a system of finite number of NODEs. This system of equations is solved numerically and the results are compared with that of the full numerical method. It was shown that the moment method is a powerful and efficient technique for the analysis of a bi-directionally pumped Raman amplifier through continuous-spectrum radiation  

The growth of slant cracks by fretting fatigue of a half plane in contact with a flat rounded pad was studied. The mode I and mode II stress intensity factors for cracks of various lengths and directions were calculated using the semi-analytical method of the distribution of dislocations, and their cumulative effect on the crack growth was investigated using the strain energy density criterion. The results showed dominance of mode I fracture on crack growth, and based on the observation of strain energy density factor versus crack orientation, the results also suggest that depending on the crack length, the most critical orientations of cracks are at 0° to 20° outward the contact zone. Good... 

In this study, a homotopy analysis method was used to obtain analytic solutions to predict dynamic pull-in instability of an electrostatically-actuated microbeam. The nonlinear describing equation of a microbeam affected by an electric field, including the fringing field effect, was obtained based on strain gradient elasticity, couple stress, and classical theory. Influences of different parameters on dynamic pull-in instability were investigated. The equation of motion of a double-clamped microbeam was discretized and solved by using Galerkin's method via mode summation. The resulting non-linear differential equation was also solved by using the Homotopy Analysis Method (HAM). The influence... 

In this paper a semi-analytical method is developed to analyze functionally graded cylindrical panels. In this method, the radial domain is divided into some finite sub-domains and the material properties are assumed to be constant in each subdomain. Imposing the continuity conditions at the interface of the adjacent sub-domains, together with the global boundary conditions, a set of linear algebraic equations are derived. Solving the linear algebraic equations, the elastic response for the thick-walled FG cylindrical panel is obtained. The method can be used for all material properties variations but in present study, material properties are assumed vary with Mori-Tanaka estimation. Results... 

In this paper, free vibration of a fiber reinforced composite cylinder in which volume fraction of its fibers vary longitudinally, is studied using a semi-analytical method. The distribution of volume fraction of fiber in base matrix is based on power law model. A micromechanical model is employed to represent its mechanical properties including elastic and physical properties of this composite cylinder. In addition, kinematically the first order shear deformation shell theory is employed for strain field. Then, weak form formulation and spatial approximations of variables are utilized to discretize the equations of motion. Different problems are solved in which primarily the validity of the... 

Diffusivity equation which can provide us with the pressure distribution, is a Partial Differential Equation (PDE) describing fluid flow in porous media. The quadratic pressure gradient term in the diffusivity equation is nearly neglected in hydrology and petroleum engineering problems such as well test analysis. When a compressible liquid is injected into a well at high pressure gradient or when the reservoir possess a small permeability value, the effect of ignoring this term increases. In such cases, neglecting this parameter can result in high errors. Previous models basically focused on numerical and semi-analytical methods for semi-infinite domain. To the best of our knowledge, no...