应用数学和力学

2012 Vol. 33, No. 11

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Properties and Appropriate Conditions of Stress Reduction Factor and Thermal Shock Resistance Parameters for Ceramics

LI Wei-guo, CHENG Tian-bao, ZHANG Ru-bing, FANG Dai-ning

2012, 33(11): 1257-1265. doi: 10.3879/j.issn.1000-0887.2012.11.001

Abstract(1643) PDF(1223)

Abstract:
Through introducing the analytical solution of the transient heat conduction problem of the plate with convection into the thermal stress field model of the elastic plate, the stress reduction factor was presented explicitly in its dimensionless form. A new stress reduction factor was introduced for the purpose of comparison. The properties and appropriate conditions of the stress reduction factor, the first and second thermal shock resistance (TSR) parameters for the high and low Biot numbers respectively, and the approximation formulas for the intermediate Biot numberinterval were discussed. To investigate the TSR of ceramics more accurately, it was recommended to combine the heat transfer theory with the theory of thermoelasticity or fracture mechanics or use a numerical method. The critical rupture temperature difference and the critical rupture dimensionless time can be used to characterize the TSR of ceramics intuitively and legibly.

Strength Differential Effect and Influence of Strength Criterion on Burst Pressure of Thin-Walled Pipelines

JIN Cheng-wu, WANG Li-zhong, ZHANG Yong-qiang

2012, 33(11): 1266-1274. doi: 10.3879/j.issn.1000-0887.2012.11.002

Abstract(1884) PDF(1174)

Abstract:
In the framework of finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to internal pressure was conducted on the basis of the unified strength criterion (USC). An analytical solution of burst pressure for pipes with capped ends was derived, which included the strength differential effect and took into account the influence of strength criterion on the burst pressure. In addition, a USC-based analytical solution of burst pressure for end-opened pipes under internal pressure was deduced. Through discussion, it is found that for the end-capped pipes the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes the burst pressure is independent of the specific form of strength criterion and strength difference in tension and compression.

State Space Solution to 3D Multilayered Elastic Soils Based on Order Reduction Method

AI Zhi-yong, CHENG Yi-chong, LIU Peng

2012, 33(11): 1275-1283. doi: 10.3879/j.issn.1000-0887.2012.11.003

Abstract(1594) PDF(1072)

Abstract:
Starting with the governing equations in terms of displacements of threedimensional elastic medium, the solutions of displacement components and their first derivatives were obtained by the application of a double Fourier transform and an order reduction method based on the CayleyHamilton theorem. Combining the solutions and the constitutive equations which connected the displacements and stresses, the transfer matrix of a single soil layer was acquired. And then the state space solution of multilayered elastic soils was further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. Numerical analysis based on the present theory was carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratum were compared and discussed.

Parametric Vibration Stability and Active Control of Nonlinear Beams

LI Feng-ming, LIU Chun-chuan

2012, 33(11): 1284-1293. doi: 10.3879/j.issn.1000-0887.2012.11.004

Abstract(2547) PDF(1236)

Abstract:
The vibration stability and active control of the parametrically excited nonlinear beam structures were studied using the piezoelectric material. The velocity feedback control algorithm was applied to obtain the active damping. The cubic nonlinear equation of motion with damping was established by employing Hamilton’ principle. The method of multiple scales was used to solve the equation of motion, and the stable region was obtained. The effects of the control gain and amplitude of the external force on the stable region and amplitudefrequency curve characteristics were analyzed numerically. From the numerical results it was seen that with the increase of the feedback control gain, the axial force to which the structure could be subjected increased, and in certain scope the structural active damping ratio also increased. With the increase of the control gain, the response amplitude decreases gradually, but the required control voltage exists peak value.

Conformal Invariance for the Nonholonomic System of Chetaev’s Type With Variable Mass

HUANG Wei-li, CAI Jian-le

2012, 33(11): 1294-1303. doi: 10.3879/j.issn.1000-0887.2012.11.005

Abstract(1983) PDF(1151)

Abstract:
Conformal invariance and conserved quantities for the nonholonomic system of Chetaev’s type with variable mass were studied. The conformal factor expressions were deduced. The necessary and sufficient conditions that the system’s conformal invariance would be Lie symmetry were obtained. The conformal invariance of weak and strong Lie symmetry for the system was given. And the system’s corresponding conserved quantities were derived. Lastly, an example was taken to illustrate the application of the result.

Dufour and Soret Effects on MHD Flow of Viscous Fluid Between Radially Stretching Sheets in a Porous Medium

M.Nawaz, T.Hayat, A.Alsaedi

2012, 33(11): 1304-1319. doi: 10.3879/j.issn.1000-0887.2012.11.006

Abstract(2160) PDF(1091)

Abstract:
The Dufour and Soret effects on the two dimensional MHD steady flow of electrically conducting viscous fluid bounded by infinite sheets were examined. An incompressible viscous fluid filled the porous space. Mathematical analysis was performed in the presence of viscous dissipation, Joule heating and first order chemical reaction. By means of suitable transformations, the governing partial differential equations through momentum, energy and concentration laws were transformed into the ordinary differential equations. The resulting equations were solved by homotopy analysis method (HAM). Convergence of the series solutions was ensured. The effects of emerging parameters on the dimensionless velocities, temperature and concentration fields were analyzed. Skin friction coefficient, Nusselt number and Sherwood number were also analyzed.

Improved Nonlinear Fluid Model in Rotating Flow

Nariman Ashrafi, Habib Karimi Haghighi

2012, 33(11): 1320-1329. doi: 10.3879/j.issn.1000-0887.2012.11.007

Abstract(1620) PDF(915)

Abstract:
Pseudoplastic circular Couette flow in annulus was investigated. The viscosity was dependent on the shear rate which directly affected the conservation equations that were solved by the spectral method in the present study. The pseudoplastic model adopted here proved suitable representative of nonlinear fluids. Unlike the previous studies where only the square of shear rate term in viscosity expression was considered to ease the numerical manipulations, in the present study the term containing the quadratic power was also taken into account. The curved streamlines of the circular Couette flow could cause a centrifugal instability leading to toroidal vortices, known as Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. Comparison with existing measurements on pseudoplastic circular Couette flow results in good agreement.

Effect of Richardson Number on Entropy Generation Over a Backward Facing Step

CHEN Sheng

2012, 33(11): 1330-1339. doi: 10.3879/j.issn.1000-0887.2012.11.008

Abstract(1548) PDF(865)

Abstract:
Flow over a backward facing step (BFS) has been taken as a useful prototype to investigate characteristics of separated flow with heat transfer. However, to date the study on the effect of Richardson number on entropy generation over BFS is absent yet although the flow pattern and heat transfer characteristic both would receive significant influence caused by variation of Richardson number in many practical applications, for example in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in BFS flow was reported for the first time. Results of entropy generation analysis was obtained by numerically solving the entropy generation equation. The values of velocity and temperature, which were the inputs of the entropy generation equation, were obtained by the lattice Boltzmann method.It is found that the distributions of local entropy generation number and Bejan number are significantly influenced by the variation of Richardson number. The total entropy generation number is a monotonic decreasing function of Richardson number whereas the average Bejan number is a monotonic increasing function of Richardson number.

Effect of Temperature Dependent Viscosity on the Revolving Axi-Symmetric Ferrofluid Flow With Heat Transfer

Paras Ram, Vikas Kumar

2012, 33(11): 1340-1351. doi: 10.3879/j.issn.1000-0887.2012.11.009

Abstract(1616) PDF(974)

Abstract:
The prime objective of the present study was to examine the effect of temperature dependent viscosity on the revolving axi-symmetric laminar boundary layer flow of incompressible, electrically nonconducting ferrofluid in the presence of a stationary plate subjected to a magnetic field and maintained at a uniform temperature. To serve this purpose, the non linear coupled partial differential equations were firstly converted into the ordinary differential equations using well known similarity transformations and later, the popular finite difference method was employed to discretize the non linear coupled differential equations. These discretized equations were then solved using Newton method in MATLAB, for which an initial guess was made with the help of Flex PDE Solver.Along with the velocity profiles, the effects of temperature dependent viscosity were also examined on skin friction, heat transfer and the boundary layer displacement thickness.The results, so obtained, were presented numerically as well as graphically.

Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method

GONG Zhao-xin, LU Chuan-jing, HUANG Hua-xiong

2012, 33(11): 1352-1365. doi: 10.3879/j.issn.1000-0887.2012.11.010

Abstract(1807) PDF(996)

Abstract:
The immersed boundary method was an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics. The effect of the regularized delta function on its accuracy was an important subject in the property study. The method of manufactured solutions was taken as the research means. The computational code was firstly verified to be mistaken free by using smooth manufactured solutions. Then a jump in the manufactured solution for pressure was introduced to study the accuracy of the immersed boundary method. Four kinds of the regularized delta function were taken to test its effects on accuracy analysis. By analyzing the discretization errors, the accuracy of the immersed boundary method was proved to be first order. Meanwhile, the results showed that the regularized delta function could not improve the accuracy, but could change the discretization errors on the entire computational domain.

Dissipative Free-Surface Solver for the Potential Flow Around a Hydrofoil Distributed With Doublets

CHEN Zhi-min, W.G.Price

2012, 33(11): 1366-1378. doi: 10.3879/j.issn.1000-0887.2012.11.011

Abstract(1583) PDF(849)

Abstract:
A doublet integral equation was formulated for a two-dimensional dissipative potential flow around a hydrofoil submerged below the free-water surface. The free-water surface was assumed to involve energy dissipation and thus was source of damping. A doublet panel method was developed from incorporation of dissipative Green function approach and doublets distribution on the hydrofoil surface. Numerical computations were implemented and derived numerical results were in good agreement with analytic solutions and experimental measurements.