非均质流固耦合介质轴对称动力问题时域解

将地基视为流固两相介质并考虑其非均质成层特性，推导了多层地基动力问题时域解．文中首先建立了一组解耦的两相介质动力控制方程；而后利用Ｌａｐｌａｃｅ－Ｈａｎｋｅｌ变换推导了单层地基象空间初参数解答；再利用初参数法及传递矩阵技术导出了任意多层地基瞬态解的一般解析算式．本文获得的解答可方便地退化为现有理想弹性介质的解答     

Large amplitude non-linear oscillations of a general conservative system

This paper presents new, approximate analytical solutions to large-amplitude oscillations of a general, inclusive of odd and non-odd non-linearity, conservative single-degree-of-freedom system. Based on the original general non-linear oscillating system, two new systems with odd non-linearity are to be addressed. Building on the approximate analytical solutions of odd non-linear systems developed by the authors earlier, we construct the new approximate analytical solutions to the original general non-linear system by combinatory piecing of the approximate solutions corresponding to, respectively, the two new systems introduced. These approximate solutions are valid for small as well as large amplitudes of oscillation for which the perturbation method either provides inaccurate solutions or is inapplicable. Two examples with excellent approximate analytical solutions are presented to illustrate the great accuracy and simplicity of the new formulation.     

Note on the Heat Transfer of Flows over a Stretching Wall in Porous Media: Exact Solutions

In this note, heat transfer over a stretching sheet with mass transfer in a porous medium is revisited. Analytical solutions are presented for two cases including a prescribed power-law wall temperature case and a prescribed power-law wall heat flux case. The solutions are expressed by the Kummer’s function. Closed-form solutions are found and presented for some special parameters. The solutions might offer more insights of the heat transfer characteristics compared with the numerical solutions.     

Generalized solutions of transient thermal shock problem with bounded boundaries

In this work, the generalized thermoelastic solutions with bounded boundaries for the transient shock problem are proposed by an asymptotic method. The governing equations are taken in the context of the generalized thermoelasticity with one relaxation time (L–S theory). The general solutions for any set of boundary conditions are obtained in the physical domain by the Laplace transform techniques. The corresponding asymptotic solutions for a thin plate with finite thickness, subjected to different sudden temperature rises in its two boundaries, are obtained by means of the limit theorem of Laplace transform. In the context of these asymptotic solutions, two specific problems with different boundary conditions have been conducted. The distributions of displacement, temperature and stresses, as well as the propagations, intersections and reflections of two elastic waves, named as thermoelastic wave and thermal wave separately, are obtained and plotted. These results are agreed with the results obtained in the existing literatures.     

Similarity solutions for power-law and exponentially stretching plate motion with cross flow

Laminar boundary layers generated by power-law plate stretching with cross flows are studied. Only the stretching solutions of Banks [10] are considered, those being bounded by exponentially stretched plates. In one case the cross flow is generated by a uniform transverse stream far above the stretching plate or a wall moving with uniform transverse velocity. Two other cases deal with cross flows generated by transverse shearing motions of the surface. Possible two parameter solutions appear, but here we present two one-parameter families of cross flow solutions generated by transverse plate shearing motion. Streamwise and transverse shear stresses and velocity profiles are displayed in graphical form.     

Functional and generalized separable solutions to unsteady Navier–Stokes equations

The paper studies unsteady Navier–Stokes equations with two space variables. It shows that the non-linear fourth-order equation for the stream function with three independent variables admits functional separable solutions described by a system of three partial differential equations with two independent variables. The system is found to have a number of exact solutions, which generate new classes of exact solutions to the Navier–Stokes equations. All these solutions involve two or more arbitrary functions of a single argument as well as a few free parameters. Many of the solutions are expressed in terms of elementary functions, provided that the arbitrary functions are also elementary; such solutions, having relatively simple form and presenting significant arbitrariness, can be especially useful for solving certain model problems and testing numerical and approximate analytical hydrodynamic methods. The paper uses the obtained results to describe some model unsteady flows of viscous incompressible fluids, including flows through a strip with permeable walls, flows through a strip with extrusion at the boundaries, flows onto a shrinking plane, and others. Some blow-up modes, which correspond to singular solutions, are discussed.     

Elastic Fields for Point and Partial Line Loading in Transversely Isotropic Linear Elasticity

In this paper some fundamental concentrated loading solutions are derived for a transversely isotropic full space. As a starting point the potential function representation for the elastic field is re-examined in light of a recent result derived by the author. It is shown that expressions for two of the stress components need to be modified from what is given in some of the existing literature. The use of these new expressions is first demonstrated by considering two point loading cases. Subsequent analysis integrates these two point force solutions over finite line segments to obtain solutions for various cases of partial line loading. The ramifications of the two modified stress equations on the partial line loading solutions are also discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Special class of solutions of the kinetic equation of a bubbly fluid

A new class of solutions is constructed for the kinetic model of bubble motion in a perfect fluid proposed by Russo and Smereka. These solutions are characterized by a linear relationship between the Riemann integral invariants. Using the expressions following from this relationship, the construction of solutions in the special class is reduced to the integration of a hyperbolic system of two differential equations with two independent variables. Exact solutions in the class of simple waves are obtained, and their physical interpretation is given.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 33–43, March–April, 2005.     

A new branch of solutions of boundary-layer flows over a permeable stretching plate

The steady-state boundary-layer flows over a permeable stretching sheet are investigated by an analytic method for strongly non-linear problems, namely the homotopy analysis method (HAM). Two branches of solutions are obtained. One of them agrees well with the known numerical solutions. The other is new and has never been reported in general cases. The entrainment velocity of the new branch of solutions is always smaller than that of the known ones. For permeable stretching sheet with sufficiently large suction of mass flux, the difference between the shear stresses and velocity profiles of two branches of solutions is obvious: the shear stress of the new branch of solutions is considerably larger than that of the known ones. However, for impermeable sheet and permeable sheet with injection or small suction of mass flux, the shear stress and the velocity profile of two branches of solutions are rather close: in some cases the difference is so small that the new branch of solutions might be neglected even by numerical techniques. This reveals the reason why the new branch of solutions has not been reported. This work also illustrates that, for some non-linear problems having multiple solutions, analytic techniques are sometimes more effective than numerical methods.     

Out-of-plane loading of anisotropic bimaterials and semi-infinite materials

Summary Analytical closed-form solutions are proposed in a rather compact form for the stress and displacement fields induced by out-of-plane loading of a semi-infinite anisotropic material with inclined strata. The solutions are then extended to include the case of a bimaterial with a planar interface. Several boundary conditions are considered for the interface which may be between two anisotropic half-planes with different elastic properties, or two different orientations of the strata in the same material.     

Unsteady shear flow of a viscoplastic material

A viscoplastic, or yield-stress, liquid occupies the space between two infinite parallel plates. Initially the whole system is at rest. The lower plate is suddenly jerked into motion with given speed or shear stress, while the upper plate is kept fixed. The flow consists of two regions; (1) a lower sheared region bounded above by the yield surface, (2) an upper unyielded region bounded below by the yield surface. The yield surface propagates to the upper plate as time proceeds. We first consider the equivalent one plate problem of flow over a jerked plate, and find similarity solutions and small time asymptotic solutions for prescribed shear and speed cases respectively. These solutions are used as initial solutions for the two plate case. The motion of the yield surface and the time taken for the entire material to yield are investigated. The problems considered here are two dimensional representations of some control devices, for example the light duty clutch, which consists of two corotating, coaxial discs separated by a layer of electrorheological material. In this application it is useful to know the time taken for all the material to yield.     

套管-水泥环-地层应力分布的理论解

利用弹性力学理论研究地应力场中套管-水泥环-地层系统应力分布的理论解，在求解过程中，将原问题分解为两个相对简单的子问题．考虑到套管井系统是层状结构的特点，且各层受力情况具有相似性，进一步地，基于两个弹性力学平面应变基本问题的解，采用结构力学的求解思想，由位移连续条件分别求得了两个子问题的解，最后由叠加原理得到了原问题的理论解．     

The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders

Numerical solutions based on the method of fundamental solutions are discussed for Stokes flow inside a rectangular cavity in the presence of circular cylinders. The Stokeslets are used as the fundamental solutions to obtain the solution for the flow field by a linear combination of fundamental solutions. Flow results on the cellular structure of flow field resulting from the dynamics of cylinders and the horizontal walls of the cavity are reported for (i) one rotating cylinder in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions, (ii) two rotating cylinders kept apart in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions. The effect of aspect ratio of the rectangular cavity, direction of movement of the two parallel horizontal sides of the cavity and the diameter of the rotating cylinder on the flow structure are studied. The flow results obtained for the single cylinder case are in accordance with the results available in the literature. From the computational point of view, the present numerical procedure based on the method of fundamental solutions is efficient and simple to implement as compared to the mesh-dependent schemes, which needs complex mesh generation procedure for the multiply connected geometrical domains considered in this article.     

Comparing analytical and numerical solution of nonlinear two and three‐dimensional hydrostatic flows

New test cases for frictionless, three‐dimensional hydrostatic flows have been derived from some known analytical solutions of the two‐dimensional shallow water equations. The flow domain is a paraboloid of revolution and the flow is determined by the initial conditions, the nonlinear advective terms, the Coriolis acceleration and by the hydrostatic pressure. Wetting and drying is also included. Some specific properties of the exact solutions are discussed under different hypothesis and relative importance of the forcing terms. These solutions are proposed for testing the stability, the accuracy and the efficiency of numerical models to be used for simulating environmental hydrostatic flows. The computed solutions obtained with a semi‐implicit finite difference—finite volume algorithm on unstructured grid are compared with the corresponding analytical solutions in both two and three space dimension. Excellent agreement are obtained for the velocity and for the resulting water surface elevation. Comparison of the computed inundation area also shows a good agreement with the analytical solution with degrading accuracy observed when the inundation area becomes relatively large and for long simulation time. Copyright © 2006 John Wiley & Sons, Ltd.     

Energetic versus maximally-dissipative local solutions of a quasi-static rate-independent mixed-mode delamination model

A quasi-static rate-independent model of delamination of linearly elastic bodies at small strains, sensitive to mode of delamination, using interfacial damage and interfacial plasticity as two internal parameters, is further developed with the aim to extract representations typically employed in engineering interface-models, i.e. fracture envelope and fracture energy dependence on the mode mixity, which are suitable for the model fitting to experimental data. Moreover, two concepts of solutions are implemented: globally stable energy-conserving solutions or stress-driven maximally-dissipative local solutions, arising by the fully implicit or by a semi-implicit time-stepping procedures, respectively, both yielding numerically stable and convergent time-discretizations. Spatial discretization is performed by the symmetric Galerkin boundary-element method (SGBEM). Alternating quadratic programming is implemented to cope with, respectively, global or local, energy-minimizations in the computation of the time-discretized solutions. Sample 2D numerical examples document applicability of the model as well as efficiency of the SGBEM numerical implementation and facilitate comparison of the two mentioned solution concepts.     

Isolated solitary vortex solutions for the Ekman Couette layer

Isolated solutions have been found describing solitary vortex motions in a fluid layer between two parallel plates moving relative to each other in a system that rotates about an axis normal to the plates. The solutions are called isolated since they do not seem to be connected by bifurcations to any other known solutions of the problem. The solitary vortex solutions are unstable with respect to three-dimensional disturbances, but attempts to find three-dimensional steady states have not yet been successful.     

Solitary waves for a nonlinear dispersive long wave equation

All the possible traveling wave solutions of Whitham-Broer-Kaup （WBK） equation are investigated in the present paper. By employing phase plane analysis, transition boundaries are derived to divide the parameter space into several regions associated with different types of phase portraits corresponding to different forms of wave solutions. All the exact expressions of bounded wave solutions are obtained as well as their existence conditions. The mechanism of bifurcation between different waves with varying Hamiltonian value has been revealed. It is pointed out that as the periods of two coexisted periodic waves tend to infinity, they may evolve to two solitary waves. Furthermore, when their trajectories pass through the common saddle point, the two solitary waves may merge into a periodic wave, and its amplitude is nearly equal to the sum of the amplitudes of the two solitary wave solutions.     

Solitary and extended waves in the generalized sinh-Gordon equation with a variable coefficient

New solitary and extended wave solutions of the generalized sinh-Gordon (SHG) equation with a variable coefficient are found by utilizing the self-similar transformation between this equation and the standard SHG equation. Two arbitrary self-similar functions are included in the known solutions of the standard SHG equation, to obtain exact solutions of the generalized SHG equation with a specific variable coefficient. Our results demonstrate that the solitary and extended waves of the variable-coefficient SHG equation can be manipulated and controlled by a proper selection of the two arbitrary self-similar functions.     

配置环形线电极的单极机中的磁流体力学流动

给出配置了环形线电极的单极机中的磁流体力学解析解. 由于问题是线性的, 求解可简化为基本解的叠加, 可利用单极机在两个区域中的基本解的衔接来求得解析解. 讨论了基本解的性质. 利用非完全电极可改善Hartmann 边界层、增加装置中的质量流量. 应用基本解讨论了连续电极的单极机.     

Multiple solutions generated by statistical linearization and their physical significance

Three cases are examined where the statistical linearization (SL) procedure can yield multiple solutions for the first and second moments of the response. The first is an oscillator with a hardening non-linear stiffness excited by a narrow-band random excitation, the second is an oscillator with two potential wells excited by wide-band random excitation, and the third is an oscillator where the non-linear features present in the first two problems are combined. The results of an SL analysis are quantitatively compared with the behaviour of digitally simulated sample functions of the displacement response. In all cases a definite correspondence is found between the occurrence of multiple solutions generated by the SL method and the appearance of noticeable jumps in sample functions of the response. In some cases a quantitative agreement exists between the first and second moment values of the multiple solutions and the magnitude of “local” moments of the response.