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2013年 第34卷 第1期    刊出日期：2013-01-03

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论文

Improved precise integration method for differential Riccati equation

高强;谭述君;钟万勰;张宏斌

2013, 34(1):  1-14.  doi:10.1007/s10483-013-1648-8

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An improved precise integration method (IPIM) for solving the differential Riccati equation (DRE) is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method (PIM) for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based on the error analysis, the criterion  for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples show that the IPIM is stable and gives the machine accuracy solutions.

New smooth gap function for box constrained variational inequalities

张丽丽;李兴斯

2013, 34(1):  15-26.  doi:10.1007/s10483-013-1649-x

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A new smooth gap function for the box constrained variational inequality problem (VIP) is proposed based on an integral global optimality condition. The smooth gap function is simple and has some good differentiable properties. The box constrained VIP can be reformulated as a differentiable optimization problem by the proposed smooth gap function. The conditions, under which any stationary point of the optimization problem is the solution to the box constrained VIP, are discussed. A simple frictional contact problem is analyzed to show the applications of the smooth gap function. Finally, the numerical experiments confirm the good theoretical properties of the method.

Neimark-Sacker (N-S) bifurcation of oscillator with dry friction in 1:4 strong resonance

郭勇;谢建华

2013, 34(1):  27-36.  doi:10.1007/s10483-013-1650-9

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An oscillator with dry friction under external excitation is considered. The Poincar´e map can be established according to the series solution near equilibrium in the case of 1:4 resonance. Based on the theory of normal forms, the map is reduced into its normal form. It is shown that the Neimark-Sacker (N-S) bifurcations may occour. The theoretical results are verified with the numerical simulations.

Surface effects of adsorption-induced resonance analysis on micro/nanobeams via nonlocal elasticity

徐晓建;邓子辰

2013, 34(1):  37-44.  doi:10.1007/s10483-013-1651-9

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The governing differential equation of micro/nanbeams with atom/molecule adsorption is derived in the presence of surface effects using the nonlocal elasticity. The effects of the nonlocal parameter, the adsorption density, and the surface parameter on  the resonant frequency of the micro/nanobeams are investigated. It is found that, in addition to the nonlocal parameter and the surface parameter, the bending rigidity and the adsorption-induced mass exhibit different behaviors with the increase in the adsorption density depending on the adatom category and the substrate material.

Electroelastic interaction between piezoelectric screw dislocation and circularly layered inclusion with imperfect interfaces

方棋洪 冯慧 刘又文

2013, 34(1):  45-62.  doi:10.1007/s10483-013-1652-6

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The interaction between a piezoelectric screw dislocation and an interphase layer in piezoelectric solids is theoretically investigated. Here, the dislocation located at arbitrary points inside either the matrix or the inclusion and the interfaces of the interphase layer are imperfect. By the complex variable method, the explicit solutions to the complex potentials are given, and the electroelastic fields can be derived from them.
The image force acting on the dislocation can be obtained by the generalized Peach- Koehler formula. The motion of the piezoelectric screw dislocation and its equilibrium positions are discussed for variable parameters. The important results show that, if the inner interface of the interphase layer is imperfect and the magnitude of degree of the interface imperfection reaches the certain value, two equilibrium positions of the
piezoelectric screw dislocation in the matrix near the interface are found for the certain material combination which has never been observed in the previous studies (without considering the interface imperfection).

State-space approach to two-temperature generalized thermoelasticity without energy dissipation of medium subjected to moving heat source

H. M. YOUSSEF

2013, 34(1):  63-74.  doi:10.1007/s10483-013-1653-7

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In this work, a model of two-temperature generalized thermoelasticity without energy dissipation for an elastic half-space with constant elastic parameters is constructed. The Laplace transform and state-space techniques are used to obtain the general solution for any set of boundary conditions. The general solutions are applied to a specific problem of a half-space subjected to a moving heat source with a constant velocity. The inverse Laplace transforms are computed numerically, and the comparisons are shown in figures to estimate the effects of the heat source velocity and the two-temperature parameter.

Exact solutions to one-dimensional transient response of incompressible fluid-saturated single-layer porous media

单振东 凌道盛 丁皓江

2013, 34(1):  75-84.  doi:10.1007/s10483-013-1654-7

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Based on the Biot theory of porous media, the exact solutions to one dimensional transient response of incompressible saturated single-layer porous media under four types of boundary conditions are developed. In the procedure, a relation between the solid displacement u and the relative displacement w is derived, and the well-posed initial conditions and boundary conditions are proposed. The derivation of the solution for one type of boundary condition is then illustrated in detail. The exact solutions for the other three types of boundary conditions are given directly. The propagation of the compressional wave is investigated through numerical examples. It is verified that only one type of compressional wave exists in the incompressible saturated porous media.

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

S. MUNAWAR A. MEHMOOD A. ALI

2013, 34(1):  85-96.  doi:10.1007/s10483-013-1655-8

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The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study. The disk impinges the oncoming flow with a time-dependent axial velocity. The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations. The governing equations are solved numerically, and two distinct similarity solution branches are obtained. Both solution branches exhibit different flow patterns. The upper branch solution exists for all values of the impinging parameter and the rotating parameter
. However, the lower branch solution breaks down at some moderate values of . The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of . The results of the velocity profile, the skin friction, and the stream lines are demonstrated through graphs and tables for both solution branches. The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.

Transient mixed convection flow arising due to thermal  and mass diffusion over porous sensor surface inside squeezing horizontal channel

M. MAHMOOD S. ASGHAR M. A. HOSSAIN

2013, 34(1):  97-112.  doi:10.1007/s10483-013-1656-6

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The double diffusion effect on the mixed convection flow over a horizontal porous sensor surface placed inside a horizontal channel is analyzed. With the appropriate transformations, the unsteady equations governing the flow are reduced to non-similar boundary layer equations which are solved numerically for the time-dependent mixed convection parameter. The asymptotic solutions are obtained for small and large values of the time dependent mixed convection parameter. The results are discussed in terms of the skin friction, the heat transfer coefficient, the mass transfer coefficient, and the velocity, temperature, and concentration profiles for different values of the Prandtl number, the Schmidt number, the squeezing index, and the mixed convection parameter.

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

丁协平

2013, 34(1):  113-126.  doi:10.1007/s10483-013-1657-x

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A new system of generalized mixed implicit equilibrium problems (SGMIEP) involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem (AMEP) is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems (SGEP) is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.