应用数学和力学

Two-Dimensional Complete Rational Analysis of Functionally Graded Beams Within the Symplectic Framework

ZHAO Li, CHEN Wei-qiu, Lü Chao-feng

2012, 33(10): 1143-1155. doi: 10.3879/j.issn.1000-0887.2012.10.001

Abstract(1944) PDF(1023)

Abstract:
Exact solutions for generally supported functionally graded plane beams were given within the framework of symplectic elasticity. The Young’s modulus was assumed to vary exponentially along the longitudinal direction while Poisson’s ratio remained constant. The state equation with a shiftHamiltonian operator matrix had been established in our previous work, but limited to the SaintVenant solution. Here it was presented that a complete rational analysis of the displacement and stress distributions in the beam by exploring the eigensolutions which were usually covered up by the SaintVenant principle. These solutions played a significant role on local behavior of materials that was usually ignored by the conventional elasticity methods but may be crucial to the failure of the materials/structures. The analysis made full use of symplectic orthogonality of the eigensolutions. Two illustrative examples were presented to compare the displacement and stress results with those for homogenous materials, and to demonstrate the effect of material inhomogeneity.

Influence of Linearly Varying Density and Rigidity on Torsional Surface Waves in an Inhomogeneous Crustal Layer

S.Gupta, S.K.Vishwakarma, D.K.Majhi, S.Kundu

2012, 33(10): 1156-1169. doi: 10.3879/j.issn.1000-0887.2012.10.002

Abstract(1766) PDF(815)

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

A Characteristic Equation Solution Strategy for Deriving the Fundamental Analytical Solutions of 3D Isotropic Elasticity

FU Xiang-rong, YUAN Ming-wu, CEN Song, TIAN Ge

2012, 33(10): 1170-1179. doi: 10.3879/j.issn.1000-0887.2012.10.003

Abstract(2490) PDF(1020)

Abstract:
A simple characteristic equation solution strategy for deriving the fundamental analytical solutions of 3D isotropic elasticity was 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 was established. Then, by substitution of the characteristic general solution vectors, which satisfied various reduced characteristic equations, into various reduced adjoint matrices of the differential operator matrix, the corresponding fundamental analytical solutions for isotropic 3D elasticity, including B-G solutions, modified P-N (P-N-W) solutions, and quasi HU Hai-chang solutions, could be obtained. Furthermore, the independence characters of various fundamental solutions in polynomial form were also discussed in details. These works provide a basis for constructing complete and independent analytical trial functions used in numerical methods.

Green’s Function Solution for Transient Heat Conduction in an Annular Fin During Solidification of a PCM

A.H.Mosaffa, F.Talati, M.A.Rosen, H.Basirat Tabrizi

2012, 33(10): 1180-1188. doi: 10.3879/j.issn.1000-0887.2012.10.004

Abstract(1923) PDF(1066)

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

Microscopic Mechanism of Periodical Electroosmosis in Reservoir Rocks

CHEN Hui, GUAN Ji-teng, FANG Wen-jing

2012, 33(10): 1189-1198. doi: 10.3879/j.issn.1000-0887.2012.10.005

Abstract(1735) PDF(817)

Abstract:
Based on the electric double layer (EDL) theory and the momentum equation governing the electroosmosis flow, an analytical solution to the periodical electroosmosis with a parallel straight capillary bundle model of reservoir rocks to reveal the microscopic mechanism of the electroosmotic flows in rocks was presented.The theory shows that both frequency dispersion characteristics of the macroscopic electroosmotic Darcy velocity in unsealed rocks and the electroosmotic pressure coefficient in sealed rocks depend 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, the greater electroosmotic Darcy velocity and the smaller electroosmotic pressure coefficient are generated. The module value of the electroosmotic Darcy velocity and the electroosmotic pressure coefficient increase with the decreasing solution concentration or the increasing cation exchange capacity without affecting the phase of the electroosmotic Darcy velocity.

Detailed Investigation Into a Single Water Molecule Entering Carbon Nanotubes

R.Ansari, E.Kazemi

2012, 33(10): 1199-1210. doi: 10.3879/j.issn.1000-0887.2012.10.006

Abstract(1951) PDF(1011)

Abstract:
The behavior of a water molecule while entering carbon nanotubes (CNTs) was studied. The LennardJones potential function together with the continuum approximation was used to obtain the van der Waals interaction between a singlewalled carbon nanotube (SWCNT) and a single water molecule. Three orientations were chosen for water molecule as the centre of mass located on the axis of nanotube. Extensive studies on the variations of force, energy and velocity distributions were performed by varying the nanotube radius and the orientations of water molecule. The force and energy distributions were validated by those obtained from molecular dynamics (MD) simulations. The acceptance radius of nanotube for sucking the water molecule inside was derived also specified in which limit of radii, nanotube was favorable to absorb water molecule. The velocities of a single water molecule while entering nanotubes were calculated and maximum entrance and interior velocity for different orientations were assigned.

Soret and Dufour Effects in the Magnetohydrodynamic(MHD) Flow of Casson Fluid

T.Hayat, S.A.Shehzad, A.Alsaedi

2012, 33(10): 1211-1221. doi: 10.3879/j.issn.1000-0887.2012.10.007

Abstract(2198) PDF(930)

Abstract:
The Soret and Dufour effects on the hydrodynamic flow of Casson fluid over a stretched surface were discussed.The relevant equations were first derived and then series solution was constructed by homotopic procedure. Results for velocity, temperature and concentration fields were displayed and discussed. Numerical values of skin friction coefficient, Nusselt and Sherwood numbers for different values of physical parameters were constructed and analyzed. Convergence of series solutions was examined.

Heat Transfer on Peristaltic Flow of Fourth Grade Fluid in an Inclined Asymmetric Channel With Partial Slip

Obaid Ullah Mehmood, Norzieha Mustapha, Sharidan Shafie

2012, 33(10): 1222-1238. doi: 10.3879/j.issn.1000-0887.2012.10.008

Abstract(1692) PDF(901)

Abstract:
The slip effects and heat transfer analysis on the peristaltic transport of magnetohydrodynamic fourth grade fluid were studied. The governing equations were first modeled and then solved under long wavelength approximation using regular perturbation method. Explicit expressions of solutions for the stream function, velocity, pressure gradient, temperature, and heat transfer coefficient were presented. Pumping and trapping phenomena were analyzed for increasing slip parameter. Further, temperature profiles and heat transfer coefficient were observed for various arising parameters. It had been found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for no-slip case were found in close agreement.

Lagrangian Cell-Centered Conservative Scheme

GE Quan-wen

2012, 33(10): 1239-1256. doi: 10.3879/j.issn.1000-0887.2012.10.009

Abstract(1773) PDF(1011)

Abstract:
A Lagrangian cell-centered conservative gas dynamics scheme was presented. It introduced the piecewise constant pressures of cell, which arose from the current time sub cell densities and the current time isentropic speed of sound of cell. The sub cell Lagrangian masses which the initial cell density multiplied by the initial sub cell volumes, divided by the current time sub cell volumes, the current time sub cell densities were obtained. Using the current time piecewise constant pressures of cell, the scheme which conserved momentum, total energy was constructed. The vertex velocities and the numerical fluxes through the cell interfaces were computed in a consistent manner due to an original solver located at the nodes. Many numerical tests were presented. They are representative test cases for compressible flows and demonstrate the robustness and the accuracy of Lagrangian cell-centered conservative scheme.

2012 Vol. 33, No. 10