Inverse electromagnetic scattering for a locally perturbed perfectly conducting plate

We consider a simple but fully three-dimensional inverse problem to determine the shape of a local perturbation of a perfectly conducting plate from far-field measurements of time harmonic electromagnetic fields. For this purpose we reformulate the model problem as an exterior Maxwell problem for a symmetric domain, and prove an equivalence between the model problem and its reformulation. Then, linear sampling method is applied to solve the reformulated problem. We illustrate the feasibility of this method by some numerical examples.     

变厚度中厚板和中厚壳的大挠度分析

采用摄动有限元法分析了变厚度中厚板和中厚壳的大挠度问题。文中借助虚功原理导出了这类板壳的一般非线性有限元方程，同时利用摄动展开求得了逐级摄动有限元的递推算式。算例表明，摄动有限元法分析变厚度中厚板壳问题同样能获得效率高精度好的结果。     

Energy functional derivative with respect to the length of a curvilinear oblique cut in the equilibrium problem for a Timoshenko plate

This paper describes the dependence of the solution of the equilibrium problem for a Timoshenko plate and the total energy functional of the plate on the perturbation of an oblique crack. The nonlinearity of the problem is caused by the boundary conditions in the form of inequalities (conditions such as the Signorini conditions), which describe mutual nonpenetration of the opposite crack faces. The continuous dependence of the solution of the problem on the perturbation of the crack length is established. A formula for the energy functional derivative of the perturbation of the crack length is obtained.     

Tension of a nonthin transversely isotropic plate with a noncircular cylindrical cavity

The three-dimensional stress state of a transversely isotropic plate with a nearly circular cylindrical cavity is examined. The cavity surface is subject to normal and tangential stresses and the plate is subject at infinity to tensile and shear forces. The problem is solved by expanding unknown functions into Fourier-Legendre series in the thickness coordinate and using the boundary-shape perturbation method. The equations and recurrence formulas needed to solve the problem in an arbitrary approximation are presented __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 101–113, November 2006.     

均变载荷下固定边圆薄板大挠度问题

关于均佈或中心集中载荷下圆薄板的大撓度平衡問題,已經有好几位学者用不同方法处理过。但用攝动法來处理时,不但計算比较簡單,并且得到的結果合乎实用。文蓀的攝动法选擇載荷为参数,解答的适用范圍小;钱偉長教授的攝动法选擇中心撓度为参数,得到的解答适用范圍大,并且和实驗的結果相符合。錢偉長教授的攝动法要比文蓀的攝动法來得高明。近几年來,錢偉长教授,胡海昌同志,叶开沅同志都采用撓皮为参数的攝动法解决了各种圓板的大撓度平衡問題。     

Reissner板弯曲问题的摄动域外奇点法

本文用摄动的方法将Ｒｅｉｓｓｎｅｒ板的变曲问题转化为一系列Ｋｉｒｃｈｏｆｆ板弯曲问题的叠加,并用后者简单的Ｇｒｅｅｎ函数按域外奇步法求解。数值算例表明,这种算法单且精度高。     

The perturbation parameter in the problem of large deflection of clamped circular plates

In the problems of large deflection of clamped circular plates under uniformly distributed loads, various perturbation parameters relating to load, deflection, slope of deflection, membrane force, etc, are studied. For a general perturbation parameter, the variational principle is used for the solution of such a problem. The applicable range of these perturbation parameters are studied in detail. In the case of uniformly loaded plate, perturbation parameter relating to central deflection seems to be the best among all others. The method of determination of perturbation solution by means of variational principle can be used to treat a variety of problems, including the large deflection problems under combine loads. This paper is completed under the guidance of Prof. Chien Wei-zang.     

Steady flows of non-Newtonian fluids past a porous plate with suction or injection

The problem of the steady flow of three classes of non-linear fluids of the differential type past a porous plate with uniform suction or injection is studied. The flow which is studied is the counterpart of the classical ‘asymptotic suction’ problem, within the context of the non-Newtonian fluid models. The non-linear differential equations resulting from the balance of momentum and mass, coupled with suitable boundary conditions, are solved numerically either by a finite difference method or by a collocation method with a B-spline function basis. The manner in which the various material parameters affect the structure of the boundary layer is delineated. The issue of paucity of boundary conditions for general non-linear fluids of the differential type, and a method for augmenting the boundary conditions for a certain class of flow problems, is illustrated. A comparison is made of the numerical solutions with the solutions from a regular perturbation approach, as well as a singular perturbation.     

局部彼得洛夫-伽辽金法分析各向异性板屈曲

基于Kirchhoff板理论和对挠度函数采用移动最小二乘近似函数进行插值，进一步研究无网格局部Petrov-Galerkin(MLPG)方法在各向异性板稳定问题中的应用．分析中，本质边界条件采用罚因子法施加，离散的特征值方程由板稳定控制方程的局部积分对称弱形式中得到．通过数值算例并与其他方法的结果进行比较，表明MLPG法求解各向异性薄板稳定问题具有收敛性好、精度高等一系列优点．     

Heat and Mass Transfer in MHD Micropolar Flow Over a Vertical Moving Porous Plate in a Porous Medium

An analysis is presented for the problem of free convection with mass transfer flow for a micropolar fluid via a porous medium bounded by a semi-infinite vertical porous plate in the presence of a transverse magnetic field. The plate moves with constant velocity in the longitudinal direction, and the free stream velocity follows an exponentially small perturbation law. A uniform magnetic field acts perpendicularly to the porous surface in which absorbs the micropolar fluid with a suction velocity varying with time. Numerical results of velocity distribution of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Also, the results of the skin-friction coefficient, the couple stress coefficient, the rate of the heat and mass transfers at the wall are prepared with various values of fluid properties and flow conditions.     

Hydroelastic stability of a rectangular plate interacting with a layer of ideal flowing fluid

The three-dimensional formulation of the problem on the natural vibrations and stability of an elastic plate which interacts with a quiescent or flowing fluid is represented and a finite element algorithm of its numerical implementation is proposed. The governing equations, which describe vortex-free ideal fluid dynamics in the case of small perturbations, are written in terms of the perturbation velocity potential and transformed using the Bubnov–Galerkin method. The plate strains are determined on the basis of the Timoshenko theory. The variational principle of virtual displacements which takes into account the work done by inertial forces and the hydrodynamic pressure is used for the mathematical formulation of the dynamic problem of elastic structure. The solution of the problem is reduced to calculations and an analysis of complex eigenvalues of a coupled system of two equations. The effect of the fluid layer height on the eigenfrequencies and the critical velocities of the loss of stability is estimated numerically. It is shown that there exist different types of instability determined by combinations of the kinematic boundary conditions prescribed at the plate edges.     

弹性板边界元中计算边界高阶导数的渐近收敛积分方程

本文针对板弯曲边界元方法中计算边界曲率等高阶导数项时边界积分方程中出现的高阶奇异积分项,通过对未知挠曲函数作渐近展开并加以适当摄动,获得了渐近收敛的边界积分方程。采用这一方法计算板边界上的曲率分布,获得了满意的数值结果。     

Dynamic behaviour of an axially moving plate undergoing small cylindrical deformation submerged in axially flowing ideal fluid

The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity.     

Solution of the plane stress problems of strain-hardening materials described by power-law using the complex pseudo-stress function

In the present paper,the compatibility equation for the plane stress problems of power-law materials is transformed into a biharmonic equation by introducing the so-calledcomplex pseudo-stress function,which makes it possible to solve the elastic-plastic planestress problems of strain hardening materials described by power-law using the complexvariable function method like that in the linear elasticity theory.By using this generalmethod,the close-formed analytical solutions for the stress,strain and displacementcomponents of the plane stress problems’of power-law materials is deduced in the paper,which can also be used to solve the elasto-plastic plane stress problems of strain-hardeningmaterials other than that described by power-law.As an example,the problem of a power-law material infinite plate containing a circular hole under uniaxial tension is solved byusing this method,the results of which are compared with those of a known asymptoticanalytical solution obtained by the perturbation method.     

On Aspects of Asymptotics for Plate Equations

In this paper some initial-boundary value problems for plate equations will be studied. These initial-boundary value problems can be regarded as simple models describing free oscillations of plates on elastic foundations or of plates to which elastic springs are attached on the boundary. It is assumed that the foundations and springs have a different behavior for compression and for extension. An approximation for the solution of the initial-boundary value problem will be constructed by using a two-timescales perturbation method. For specific parameter values it turns out that complicated internal resonances occur.     

Buckling delamination of a rectangular plate containing a rectangular crack and made from elastic and viscoelastic composite materials

This paper studies a three-dimensional buckling delamination problem for a rectangular plate made from elastic and viscoelastic composite material. It is assumed that the plate contains a rectangular band-crack (Case 1) and a rectangular edge-crack (Case 2) and that the edge-surfaces of these cracks have an initial infinitesimal imperfection. The evolution of this initial imperfection with an external compressive loading, acting along the crack (for an elastic composite) or with duration of time (for a viscoelastic composite under fixed external loading) is investigated within the framework of three-dimensional geometrically non-linear field equations of the theory of the viscoelasticity for anisotropic bodies. To determine the values of the critical force or critical time as well as the buckling delamination mode, the initial imperfection criterion is used. The corresponding boundary-value problems are solved by employing boundary form perturbation techniques, Laplace transform and FEM (Finite Element Method). The influence of the materials and/or the geometrical parameters of the plate on the critical values are discussed. In particular, it is established that for the considered change range of the problem parameters, the buckling form depends only on the initial infinitesimal imperfection mode of the crack edges.     

Dynamics stress concentrations in Ambartsumian's plate with a cutout

Based on the motion equations of flexural wave in Ambartsumian's plates including the effects of transverse shear deformations, by using perturbation method of small parameter, the scattering of flexural waves and dynamic stress concentrations in the plate with a cutout have been studied. The asymptotic solution of the dynamic stress problem is obtained. Numerical results for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutour are graphically presented and discussed. The project supported by the National Natural Science Foundation of China.     

Analysis of the transpiration cooling of a thin porous plate in a hot laminar convective flow

This paper deals with the asymptotic and numerical analysis for the steady-state transpiration cooling of a thin porous flat plate in a laminar hot convective flow, taking into account the streamwise heat conduction through the plate. For high conductivity plates, a regular perturbation analysis has been carried out, yielding a three-term asymptotic solution for the distribution of plate temperature. In the limit of a very poorly conducting plate, a singular perturbation technique, based on matched asymptotic expansions, is employed to solve the governing equations. We also solved the equations numerically using a quasilinearization technique. The numerical results are in good agreement with the asymptotic solution close to the asymptotic limits studied.     

Non-symmetrical large deformation of a shallow thin conical shell

I.IntroductionItisimportanttoresearchnon-symmetricalquestionsofshallowcollicalshellsintheoryoronapplication.Asonekindofpressurevessel'sparts,shallowconicalshellsareverycommonlyusedillellgineerillgpractice,becausethedifficultyofmanul\lctul.illgthemis'small.AlthotlghwelookupmanyChineseandtbreignperiodicalswhicharctlblctobefound,wehavenotyeth'ulldarticlesanddocumentsfornon-symmetricalandnolllinearquestionsofshitllowconictllshells.Oval'rccelltyears,ProlbssorWangXinzhiandhiscolleagueshavedonealot…