Sharif Digital Repository

The square G2 of a graph G is a graph with the same vertex set as G in which two vertices are joined by an edge if their distance in G is at most two. For a graph G, χ[G2), which is also known as the distance two coloring number of G is studied. We study coloring the square of grids Pm□Pn, cylinders Pm□C n, and tori Cm□Cn. For each m and n we determine χ((Pm□Pn)2), χ(P m□Cn)2), and in some cases χ((C m□Cn)2) while giving sharp bounds to the latter. We show that χ((Cm□Cn)2) is at most 8 except when m -n = 3, in which case the value is 9. Moreover, we conjecture that for every m (m ≥ 5) and n (n ≥ 5), we have, 5 ≤ χ((Cm□Cn)2) ≤ 7  

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... 

The isomerization of D-glucose to D-fructose using the immobilized glucose isomerase, as a typical model system of solid-liquid enzyme reactions has been carried out in a novel type of two-impinging-jets reactor (TIJR), which is characterized by a rotating inner cylinder in a stationary one. Because of the impinging process, turbulence, and complex trajectory of the solid particles within the reactor, the fractional conversion of glucose obtained in the TIJR increased dramatically compared to that obtained by conventional reaction systems. A compartment model was considered to describe the pattern of flow [residence time distribution (RTD) of solid particles] within the TIJR. Considering... 

In this paper, using an analytical optimization method, optimum design of multi-layer compound cylinders with different materials in layers is investigated. For this purpose, considering Tresca criterion, maximum shear stress in each layer is minimized. At the optimum condition, the maximum shear stress at all layers occurs simultaneously. The general analytical relations for optimum dimension of layers, residual pressures and radial interferences are derived. The existence condition of the optimum solution is also investigated and the constraints for materials selection are derived too. It is shown that the allowable shear stress ratio of materials must be close to their geometric mean... 

It is well established that nanofluids increase or decrease heat transfer in boiling phenomenon. The study acquired Quenching curve and boiling curve in two different surface roughnesses in two fluids: deionized water and the nanofluid MWCNT-water with four different concentrations. The cylinder was made of silver and two surface roughnesses of 129 and 690 nm. It was heated up and soaked in the fluid mentioned above. Temperature was recorded by a drilled to install thermocouple. The experiment was replicated in five times. To calculate the heat transfer quotient, assuming the cylinder to be thermally homogeneous, the Lumped capacity method was applied. The obtained results during quenching... 

We extend a hybrid DSMC/Navier-Stokes (NS) approach to unify the DSMC and the NS simulators in one framework capable of solving the mixed non-equilibrium and near-equilibrium flow regions efficiently. Furthermore, we use a one-way state-based coupling (Dirichlet-Dirichlet boundary-condition coupling) to transfer the required information from the continuum region to the rarefied one. The current hybrid DSMC-NS frame is applied to the hypersonic flows over nanoflat plate and microcylinder cases. The achieved solutions are compared with the pure DSMC and NS solutions. The results show that the current hybrid approach predicts the surface heat transfer rate and shear stress magnitudes very... 

In this paper, the whirling frequencies of simply supported and clamped rotating cylindrical shells surrounded by an elastic foundation are investigated. The Love's shell theory is used along with the Winkler foundation to obtain the governing equations of motion. An exact power series solution is obtained for arbitrary boundary conditions and the results are verified with the literature. Several case studies are performed, and the effect of spinning speed, foundation stiffness, and geometrical dimensions of the cylinder on the whirling frequencies are investigated  

In this paper, employing an analytical method, optimum design of multi-layer compound cylinders is investigated. To this end, considering Tresca criterion, maximum shear stress in each layer is minimized. Analytical relations for optimum values of a layer dimension, residual pressures and radial interferences are derived. A technique for shrink-fitting of layers is also proposed and relationships for radial interferences, residual pressures and required temperature differences during the shrink-fitting process are derived. Three different examples are presented to show the effectiveness of the proposed method. It is shown that increasing the number of layers makes shear stress distribution... 

A series of experimental and numerical investigations on two tandem cylinders wake have been studied. The velocity profile and turbulence intensity have been acquired by a single one dimensional Hot Wire anemometer. The two cylinders were mounted in a tandem manner in the horizontal mid plane of the working section. The effect of the upstream cylinder diameter, Reynolds number and the distance between the cylinders on the wake profile and turbulence intensity on the downstream cylinder was investigated, while the Reynolds number ranged between1.5× (10)∧4 ∼ 3×(10)∧4. The upstream cylinder diameter (d) was 10, 20 and 25 mm, while the downstream cylinder diameter (D) was 25 mm, corresponding to... 

Modern Latticed composite materials whose high specific strength and stiffness are utilized in spacecraft and rocket structures to a sufficiently high extent are now widely used in primary airframe structures. In this work a comparison between squared latticed composite cylinder shells and the equivalent hollow cylinder with same weight, outer radius, length and material is done. An analytical equation is derived for natural frequency of square latticed composite shells. The first fifth modes are taken to be compared. The analytical and FEM results are shown and compared to each other. Also, as discussed, the squared lattice cylinder shell reaches to their natural frequencies easily than the... 

A sixteen node cylindrical super element is presented for evaluating the free vibration characteristics of a rotating laminated cylinder with conventional boundary conditions. It is shown that the natural frequencies are affected considerably when the centrifugal force is also taken into account. The vibration frequencies of rotating finite cylinder, obtained by conventional finite element are used to evaluate the accuracy of this approach. The special case of a stationary cylinder with zero spinning velocity is also considered as a check on this method. Results indicate only few number of cylindrical super elements are capable of predicting the natural frequency of the rotating cylinder... 

It has been shown that nanofluids in different investigations increase or decrease heat transfer rate in boiling phenomenon. The present study examined the effects of ferro-fluid concentrations and magnetic field implementation on the fluid throughout the boiling process. Obtained are the quenching curve and boiling curve on specified surface roughness in both water and ferro-fluid with two different concentrations. A silver cylinder with Aspect ratio of 10, and surface roughness of 689 nm was heated up to 350 C and then was overwhelmed in the fluid under study. Temperatures were measured by a thermocouple which installed in the center of the cylinder. The test was carried out 5 times. The... 

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the... 

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 paper, strain gradient thermo-elasticity formulation for axisymmetric Functionally Graded (FG) thick-walled cylinders is presented. For this purpose, the elastic strain energy density function is considered to be a function of gradient of strain tensor in addition to the strain tensor. The material properties are assumed to vary according to a power law in radial direction. Using the constitutive equations and equation of equilibrium in the cylindrical coordinates, a fourth order non-homogenous governing equation for thermo-elastic analysis of thick-walled FG cylinders subjected to thermal and mechanical loadings is obtained and solved numerically. Results show that the intrinsic... 

Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer... 

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... 

In this paper, based on the high-order theory (HOT) of sandwich structures, the response of sandwich cylindrical shells with flexible core and any sort of boundary conditions under a general distributed static loading is investigated. The faces and the core are made of isotropic materials. The faces are modeled as thin cylindrical shells obeying the Kirchhoff–Love assumptions. For the core material, it is assumed to be thick and the in-plane stresses are negligible. The governing equations are derived using the principle of the stationary potential energy. Using harmonic differential quadrature method (HDQM), the equations are solved for deformation components. The obtained results are... 

The objective of this study is to develop a general finite element formulation associated with an incremental adaptive procedure which established for thermoviscoelastic stress analysis of orthotropic cylinders made of polymers. This paper concerned with development of a numerical algorithm for the solution of the quasistatic initial/boundary value problems involving the linear viscoelastic media with thermal and mechanical deformations. The viscoelastic constitutive equations, represented in an integral form and involving relaxation functions, are transformed into an incremental algebraic relation. An incremental relaxation is then developed for the finite element formulation to deal with... 

In this paper, the well-known effective medium approximation (EMA) and coupled dipole approximation (CDA) methods are employed to study the optical properties of a metal nanoparticle-block copolymer (MNP-BCP) nanocomposite. This approach is applied to study a system consisting of small gold spherical nanoparticles randomly distributed in the cylindrical micelles of a di-BCP. At first, the EMA method is used to obtain the effective dielectric function of a semi-metallic cylinder. Then, the extinction spectrum of the hexagonal 2D-array of semi-metallic cylinders is obtained by the CDA method. This procedure makes it possible to study simultaneously both the electromagnetic extinction of MNPs...