Applied Mathematics and Mechanics (English Edition)

Properties and appropriate conditions of stress reduction factor and thermal shock resistance parameters for ceramics

李卫国;成天宝;张如炳;方岱宁

2012, 33(11): 1351-1360. doi:10.1007/s10483-012-1627-x

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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 is presented explicitly in its dimensionless form. A new stress reduction factor is 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 are discussed. To investigate the TSR of ceramics more accurately, it is 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

金乘武;王立忠;张永强

2012, 33(11): 1361-1370. doi:10.1007/s10483-012-1628-7

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In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion (USC). An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USCbased analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By 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 the strength criterion and strength difference in tension and compression.

State space solution to 3D multilayered elastic soils based on order reduction method

艾智勇;成怡冲;刘鹏

2012, 33(11): 1371-1380. doi:10.1007/s10483-012-1629-8

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Starting with the governing equations in terms of displacements of 3D elastic media, the solutions to displacement components and their first derivatives are 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 connect the displacements and stresses, the transfer matrix of a single soil layer is acquired. Then, the state space solution to multilayered elastic soils is further obtained by introducing the boundary conditions and continuity conditions between adjacent soil layers. The numerical analysis based on the present theory is carried out, and the vertical displacements of multilayered foundation with a weak and a hard underlying stratums are compared and discussed.

Parametric vibration stability and active control of nonlinear beams

李凤明;刘春川

2012, 33(11): 1381-1392. doi:10.1007/s10483-012-1630-6

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

Conformal invariance for nonholonomic system of Chetaev’s type with variable mass

黄卫立;蔡建乐

2012, 33(11): 1393-1402. doi:10.1007/s10483-012-1631-7

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Conformal invariance and conserved quantities for a nonholonomic system of Chetaev’s type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system’s conformal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

M. NAWAZ;T. HAYAT;A.ALSAEDI

2012, 33(11): 1403-1418. doi:10.1007/s10483-012-1632-6

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The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.

Improved nonlinear fluid model in rotating flow

N. ASHRAFI;H. KARIMI-HAGHIGHI

2012, 33(11): 1419-1430. doi:10.1007/s10483-012-1633-x

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The pseudoplastic circular Couette flow (CCF) in annuli is investigated. The viscosity is dependent on the shear rate that directly affects the conservation equations solved by the spectral method in the present study. The pseudoplastic model adopted here is shown to be the suitable representative of nonlinear fluids. Unlike the previous studies, where only the square of the shear rate term in the viscosity expression is considered to ease the numerical manipulations, in the present study, the term containing the quadratic power is also taken into account. The curved streamlines of the CCF can cause the centrifugal instability leading to toroidal vortices, known as the Taylor vortices. It is further found that the critical Taylor number becomes lower as the pseudoplastic effect increases. The comparison with the existing measurements on the pseudoplastic CCF results in good agreement.

Effect of Richardson number on entropy generation over backward facing step

陈胜

2012, 33(11): 1431-1440. doi:10.1007/s10483-012-1637-8

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The flow over a backward facing step (BFS) has been taken as a useful prototype to investigate intrinsic mechanisms of separated flow with heat transfer. However, to date, the open literature on the effect of Richardson number on entropy generation over the BFS is absent yet, although the flow pattern and heat transfer characteristic both will receive significant influence caused by the variation of Richardson number in many practical applications, such as in microelectromechanical systems and aerocrafts. The effect of Richardson number on entropy generation in the BFS flow is reported in this paper for the first time. The entropy generation analysis is conducted through numerically solving the entropy generation equation. The velocity and temperature, which are the inputs of the entropy generation equation, are evaluated 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 revolving axi-symmetric ferrofluid flow with heat transfer

P. RAM;V. KUMAR

2012, 33(11): 1441-1452. doi:10.1007/s10483-012-1634-8

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The prime objective of the present study is to examine the effect of temperature dependent viscosity μ(T) on the revolving axi-symmetric laminar boundary layer flow of an 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 are firstly converted into the ordinary differential equations using well-known similarity transformations. The popular finite difference method is employed to discretize the non-linear coupled differential equations. These discretized equations are then solved using the Newton method in MATLAB, for which an initial guess is made with the help of the Flex PDE Solver. Along with the velocity profiles, the effects of temperature dependent viscosity are also examined on the skin friction, the heat transfer, and the boundary layer displacement thickness. The obtained results are presented numerically as well as graphically.

Effect of regularized delta function on accuracy of immersed boundary method

宫兆新;鲁传敬;黄华雄

2012, 33(11): 1453-1466. doi:10.1007/s10483-012-1635-9

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The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics. The effect of the regularized delta function on the accuracy is an important subject in the property study. A method of manufactured solutions is used in the research. The computational code is first verified to be mistake-free by using smooth manufactured solutions. Then, a jump in the manufactured solution for pressure is introduced to study the accuracy of the immersed boundary method. Four kinds of regularized delta functions are used to test the effect on the accuracy analysis. By analyzing the discretization errors, the accuracy of the immersed boundary method is proved to be first-order. The results show that the regularized delta function cannot improve the accuracy, but it can change the discretization errors in the entire computational domain.

Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets

陈志敏;W. G. PRICE

2012, 33(11): 1467-1480. doi:10.1007/s10483-012-1636-9

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

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