Applied Mathematics and Mechanics (English Edition)

In Memory of the 100th Anniversary of Professor Wei-zang CHIEN

Editorial Board of Applied Mathematics and Mechanics

2012, 33(10): 1223-1224. doi:10.1007/s10483-012-1626-8

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October 9 of this year is the 100th anniversary of Professor Wei-zang CHIEN, who was the founder of our journal Applied Mathematics and Mechanics.

Two-dimensional complete rational analysis of functionally graded beams within symplectic framework

赵莉;陈伟球;吕朝锋

2012, 33(10): 1225-1238. doi:10.1007/s10483-012-1617-8

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Exact solutions for generally supported functionally graded plane beams are given within the framework of symplectic elasticity. The Young’s modulus is assumed to exponentially vary along the longitudinal direction while Poisson’s ratio remains constant. The state equation with a shift-Hamiltonian operator matrix has been established in the previous work, which are limited to the Saint-Venant solution. Here, a complete rational analysis of the displacement and stress distributions in the beam is presented by exploring the eigensolutions that are usually covered up by the Saint-Venant principle. These solutions play a significant role in the local behavior of materials that is usually ignored in the conventional elasticity methods but possibly crucial to the materials/structures failures. The analysis makes full use of the symplectic orthogonality of the eigensolutions. Two illustrative examples are presented to compare the displacement and stress results with those for homogenous materials, demonstrating the effects of material inhomogeneity.

Influence of linearly varying density and rigidity on torsional surface waves in inhomogeneous crustal layer

S. GUPTA;S. K. VISHWAKARMA;D. K. MAJHI;S. KUNDU

2012, 33(10): 1239-1252. doi:10.1007/s10483-012-1618-7

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The present work deals with the possibility of propagation of torsional surface wave in an inhomogeneous crustal layer over an inhomogeneous half space. The layer has inhomogeneity which varies linearly with depth whereas the inhomogeneous half space exhibits inhomogeneity of three types namely exponential, quadratic, and hyperbolic discussed separately. Dispersion equation is deduced for each case in a closed form. For a layer over a homogeneous half space, the dispersion equation agrees with the equation of the classical case. It is observed that the inhomogeneity factor due to linear variation in density in the inhomogeneous crustal layer decreases as the phase velocity increases, while the inhomogeneity factor in rigidity has the reverse effect on the phase velocity.

Characteristic equation solution strategy for deriving fundamental analytical solutions of 3D isotropic elasticity

傅向荣;袁明武;岑松;田歌

2012, 33(10): 1253-1264. doi:10.1007/s10483-012-1619-7

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A simple characteristic equation solution strategy for deriving the fun- damental analytical solutions of 3D isotropic elasticity is proposed. By calculating the determinant of the differential operator matrix obtained from the governing equations of 3D elasticity, the characteristic equation which the characteristic general solution vectors must satisfy is established. Then, by substitution of the characteristic general solution vectors, which satisfy various reduced characteristic equations, into various reduced ad- joint matrices of the differential operator matrix, the corresponding fundamental analyt- ical solutions for isotropic 3D elasticity, including Boussinesq-Galerkin (B-G) solutions, modified Papkovich-Neuber solutions proposed by Min-zhongWANG (P-N-W), and quasi HU Hai-chang solutions, can be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form are also discussed in detail. These works provide a basis for constructing complete and independent analytical trial func- tions used in numerical methods.

Green’s function solution for transient heat conduction in annular fin during solidification of phase change material

A. H. MOSAFFA;F. TALATI;M. A. ROSEN;H. BASIRAT-TABRIZI

2012, 33(10): 1265-1274. doi:10.1007/s10483-012-1620-x

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The Green’s function method is applied for the transient temperature of an annular fin when a phase change material (PCM) solidifies on it. The solidification of the PCMs takes place in a cylindrical shell storage. The thickness of the solid PCM on the fin varies with time and is obtained by the Megerlin method. The models are found with the Bessel equation to form an analytical solution. Three different kinds of boundary conditions are investigated. The comparison between analytical and numerical solutions is given. The results demonstrate that the significant accuracy is obtained for the temperature distribution for the fin in all cases.

Microscopic mechanism of periodical electroosmosis in reservoir rocks

陈辉;关继腾;房文静

2012, 33(10): 1275-1286. doi:10.1007/s10483-012-1621-9

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Based on the electric double layer (EDL) theory and the momentum equation governing the electroosmosis flow, this paper presents an analytical solution to the peri- odical electroosmosis with a parallel straight capillary bundle model of reservoir rocks to reveal the microscopic mechanism of the electroosmotic flows in rocks. The theory shows that both the frequency dispersion characteristics of the macroscopic electroosmotic Darcy velocity in unsealed rocks and the electroosmotic pressure coefficient in sealed rocks de- pend on the porosity and electrochemical properties of reservoir rocks. The mathematical simulation indicates that the distribution of the periodical electroosmotic velocity is wave- like in the rock pore. The greater the porosity is, the greater electroosmotic the Darcy velocity and the smaller electroosmotic pressure coefficient are generated. The module values of the electroosmotic Darcy velocity and the electroosmotic pressure coefficient increase with the decreasing solution concentration or the increasing cation exchange ca- pacity without affecting the phase of the electroosmotic Darcy velocity.

Detailed investigation on single water molecule entering carbon nanotubes

R. ANSARI;E. KAZEMI

2012, 33(10): 1287-1300. doi:10.1007/s10483-012-1622-8

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The behavior of a water molecule entering carbon nanotubes (CNTs) is stud- ied. The Lennard-Jones potential function together with the continuum approximation is used to obtain the van der Waals interaction between a single-walled CNT (SWCNT) and a single water molecule. Three orientations are chosen for the water molecule as the center of mass is on the axis of nanotube. Extensive studies on the variations of force, energy, and velocity distributions are performed by varying the nanotube radius and the orientations of the water molecule. The force and energy distributions are validated by those obtained from molecular dynamics (MD) simulations. The acceptance radius of the nanotube for sucking the water molecule inside is derived, in which the limit of the radius is specified so that the nanotube is favorable to absorb the water molecule. The velocities of a single water molecule entering CNTs are calculated and the maximum entrance and the interior velocity for different orientations are assigned and compared.

Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid

T. HAYAT;S. A. SHEHZAD;A. ALSAEDI

2012, 33(10): 1301-1312. doi:10.1007/s10483-012-1623-6

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This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined.

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

O. U. MEHMOOD;N. MUSTAPHA;S. SHAFIE

2012, 33(10): 1313-1328. doi:10.1007/s10483-012-1624-6

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In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

Lagrangian cell-centered conservative scheme

葛全文

2012, 33(10): 1329-1350. doi:10.1007/s10483-012-1625-9

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This paper presents a Lagrangian cell-centered conservative gas dynamics scheme. The piecewise constant pressures of cells arising from the current time sub-cell densities and the current time isentropic speed of sound are introduced. Multipling the initial cell density by the initial sub-cell volumes obtains the sub-cell Lagrangian masses, and dividing the masses by the current time sub-cell volumes gets the current time sub- cell densities. By the current time piecewise constant pressures of cells, a scheme that conserves the momentum and total energy is constructed. The vertex velocities and the numerical fluxes through the cell interfaces are computed in a consistent manner due to an original solver located at the nodes. The numerical tests are presented, which are representative for compressible flows and demonstrate the robustness and accuracy of the Lagrangian cell-centered conservative scheme.

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