Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

Load motion along a beam on a viscoelastic half-space

An expression is derived for equivalent foundation of a viscoelastic half-space interacting with an Euler–Bernoulli beam. It is shown that this equivalent viscoelastic foundation depends on frequencies and wave numbers of the waves in the beam. The real and imaginary part of it substantially varies for phase velocities in between the Rayleigh and shear waves velocities. Radiation of elastic waves occurs for velocities larger than some velocity in that interval. The steady-state beam displacements due to a uniformly moving constant load are calculated for different velocities. The maximum displacement under the load takes place for a velocity of order of the Rayleigh waves velocity.     

Quasi-static response of linear viscoelastic cantilever beams subject to a concentrated harmonic end load

This study evaluates the response of a uniform cantilever beam with a symmetric cross-section fixed at one end, and submitted to a lateral concentrated sinusoidal load at the free extremity. The beam material is assumed to be homogeneous, isotropic and linear viscoelastic. Due to the nature of the loading and the beam slenderness, large displacements are developed but the strains are considered small. Consequently, the mathematical formulation only involves geometrical non-linearity. It is also assumed that the beam is inextensible (neutral axis length is constant) and that inertial forces are negligible, i.e., dynamic effects are insignificant and the system can thus be modeled quasi-statically. The beam is therefore subject to oscillations caused by the sinusoidal time-dependent load, leading to a transient response until the material stabilizes and the system exhibits a periodic response, which can be conveniently described in the frequency domain. The time domain solution of this problem is elaborated by considering the quasi-static response for each time interval. The mathematical equations are presented in dimensional and dimensionless forms, and for the latter case, a numerical solution is generated and several case studies are presented. The problem is governed by a set of non-linear ordinary differential equations encompassing functions of space and time that relate the curvature, rotation angle, bending moment and geometrical coordinates. In this study, an elegant solution is deduced using perturbation theory, yielding a precise steady-state solution in the frequency domain with considerable computational economy. The solutions for both time and frequency domain methods are developed and compared using a case study for a series of dimensionless parameters that influence the response of the system.     

Radiation emitted by a constant load moving uniformly in a circle on an elastically supported membrane

Wave radiation is studied which is due a constant load moving with a constant speed along a circular path over an unbounded membrane on a elastic foundation. The steady-state solution of the problem is obtained, showing that the radiation occurs for all load velocities. It is shown that the elastic field radiated by the supercritically moving load is confined in a spiral-like apex. The membrane displacements at the boundaries of this apex are discontinuous. The radiated energy per period of load rotation is calculated showing a discrete energy spectrum. For increasing load velocities, the total amount of radiated energy becomes larger. It also turns out that the major part of the radiated energy follows the direction of the load motion.     

THE ANALYSIS OF INTERLAMINAR STRESSES FOR COMPOSITE LAMINATED SHALLOW SHELLS WITH INTERFACIAL DAMAGE

Based on the general six-degrees-of-freedom plate theory towards the accurate stress analysis and nonlinear theory of shallow shells, considering the damage effect of the interlaminar interface and using the variation principle, the three-dimensional non-linear equilibrium differential equations of the laminated shallow shells with interfacial damage are derived. Then, considering a simply supported laminated shallow shell with damage and under normal load, an analytical solution is presented by using finite difference method to obtain the interlaminar stresses. Numerical results show, the stiffness of the shell is weakened, greater absolute values of displacements as well as smaller interlaminar stresses are obtained by interfacial damage. When the interfacial damage is further increased, delamination occurs obviously under normal pulling load and pure shear slip occurs under normal pressure load. The portion of the load undertaken by the two sides of the interface is more different. Different mechanical behaviors are shown in both sides of the interface, and the discontinuation of stresses and displacements takes place in the interface.     

移动载荷作用下沥青路面稳态响应与计算

为了研究移动载荷作用下沥青路面稳态响应,将沥青路面看作为作用在Kelvin黏弹性地基 上不仅具有弹性而且具有黏滞性的无限长梁,建立了梁的稳态响应数学模型. 找到了稳态响 应与瞬态响应的关系,由瞬态响应解析解得到了稳态响应近似解析解,并进行了实例计算. 从而解决了稳态数学模型难以求解和计算的问题. 计算结果表明,依所给的道路参数和车辆 载荷,只要响应位置距初始位置一定距离,移动载荷作用下沥青路面的瞬态响应即为稳态 响应.     

预应力条件下轴对称圆板的响应解

本文研究预应力条件下轴对称简支和固支圆板的瞬态响应,利用振型展开和Laplace变换给出解析表达式,提出简化型圆板的边界条件,利用Hankel变换和Laplace变换给出简捷的解,针对几种边界状态,比较了其频率和响应,同时讨论了几种常见的瞬态载荷的结构响应形式。     

The dynamic response of a strain-softening beam

The dynamic response of a strain-softening beam subjected to a transverse impulsive on its tip is investigated. A softening moment-curvature relation is assumed for the beam and a closed form solution is obtained for a special kind of load, which shows that there exists a softening region in the beam and this region propagates along the beam. This result indicates that, except for the possible discrete softening points with rotation discontinuity caused by the deformation localization^[1], the existence of the softening region and its travelling along the beam are the essential features of the dynamic response of a strain-softening beam. The results also show that the failure of the beam should take place under a special load and the critical condition on which the dynamic failure occurs is given. The project supported by National Natural Science Foundation of China     

厚圆板轴对称振动的弹性力学解

本文以轴对称三维弹性力学基本方程为基础,导出厚圆板强迫振动的状态方程式。利用Ｍａｃｌａｕｒｉｎ级数和Ｓｙｌｖｅｓｔｅｒ定理,厚圆板的位移和应力可以用中面位移和应力的微分算子表示。通过载荷分解和圆板表面条件,可以得到厚圆板在对称载荷与反对称载荷作用下的振动控制方程。求解了厚圆板在周边固支和简支条件下的对称与反对称的自由振动问题。通过数值计算得到了这两类自由振动的固有频率。本文的方法适用于求解厚圆板在     

Nonlinear waves generated by a steadily moving line load on an elastic plate

The steady-state response of an infinite plate to a steadily moving line load is studied. The nonlinear plate theory of Herrmann is used. The plate response is governed by a set of nonlinear differential equations and, in addition, must satisfy the “radiation” conditions. Appropriate radiation conditions for the present nonlinear problem are developed. Exact solutions representing nonlinear waves generated by the moving load are constructed.     

Benchmark trigonometric and 3-D elasticity solutions for an exponentially graded thick rectangular plate

The bending problem of a transverse load acting on an isotropic inhomogeneous rectangular plate using both two-dimensional (2-D) trigonometric and three-dimensional (3-D) elasticity solutions is considered. In the present 2-D solution, trigonometric terms are used for the displacements in addition to the initial terms of a power series through the thickness. The effects due to transverse shear and normal deformations are both included. The form of the assumed 2-D displacements is simplified by enforcing traction-free boundary conditions at the faces of the plate. No transverse shear correction factors are needed because a correct representation of the transverse shearing strain is given. The plate material is exponentially graded, meaning that Lamé’s coefficients vary exponentially in a given fixed direction (the thickness direction). A wide variety of results for the displacements and stresses of an exponentially graded rectangular plate are presented. The validity of the present 2-D trigonometric solution is demonstrated by comparison with the 3-D elasticity solution. The influence of aspect ratio, side-to-thickness ratio and the exponentially graded parameter on the bending response are investigated.     

Explicit solutions for depressed masonry arches loaded until collapse—Part I: a one-dimensional nonlinear elastic model

In this paper the equilibrium problem for masonry arches is formulated in terms of a suitable set of nonlinear ordinary differential equations. We show that by making a small number of simple hypotheses it is possible to find the explicit expressions for the displacements and rotations of the cross-sections of an in-plane loaded masonry arch. To this end, the masonry arch is schematised as a curved, one-dimensional nonlinear elastic beam made of a material that is by hypothesis incapable of withstanding significant tensile stresses. In this first part of the two-part paper, the one-dimensional model and the explicit expressions for the displacements and rotations, obtained by integrating the set of differential equations, are presented. In particular, the formal expressions for displacement, stress and strain fields are illustrated in full detail for an explicit, albeit approximate, solution for a statically determinate depressed arch subjected to a uniform vertical load.     

A knife-edge load traveling on the surface of an elastic halfspace

A load moving on the surface of an elastic halfspace forms a basic problem that is related to different fields of engineering, such as the subsoil response due to vehicle motion or the ultrasound field due to an angle beam transducer. Many numerical techniques have been developed to solve this problem, but these do not provide the fundamental physical insights that are offered by closed form solutions, which are very rare in comparison. This paper describes the development and analysis of the closed form space-time domain solution for a knife-edge load, i.e. a line segment of normal traction, moving at a constant speed on the surface of an elastic halfspace. The various contributions making up the exact solution, obtained with the Cagniard-De Hoop method, produce all the complicated wave patterns from this distributed type of loading. Examples are the transient wave field at the starting position of the load, angled conical and plane waves propagating into the solid, Rayleigh waves propagating along the surface, and head waves spreading and attenuating in specific directions from the loading path. The influence of the load speed on the wave field is investigated by considering the singularities in the relevant complex domains, for each sonic range relative to the bulk wave velocities. The characteristic wave fronts and wave patterns as exhibited by the particle displacements are evaluated for subsonic, transonic and supersonic load speeds.     

滑动最小二乘插值函数配点法

给出了利用滑动最小二乘法构造加权残值法中试函数的方法，对试函数中的基函数以及权函数的选取提出了建议；该试函数适用于任何定解问题，采用配点法求出试函数中的系数，进而可得到定解问题的近似解，利用该试函数对简支板的挠曲，悬臂梁的弯曲，以及中心具有小圆孔的大板的均匀拉伸等三个例子进行了数值计算，并与理论结果进行对比，同时还检验了该法的精度对结点数，配点数，以及结点影响半径的依赖情况，结果表明，该试函数适用于多种边值问题，且精度高，该法简化了选择试函数的过程，尤其适用于工程中的各种数值计算。     

Stress wave propagation in plates subjected to a transient line source

A method of treating the response of plates to a transient load, which was recently proposed, is here elaborated for the particular case of a plate subjected to a transient line source. Expressions presenting the various stresses as functions of time and position are derived. A numerical scheme, by which these stresses are calculated, is described. Some results concerning the behavior of stresses in the course of time are illustrated and discussed.     

饱和土体中圆柱形孔洞的动力分析

本文采用工程通用的土力学模型，利用积分变换法推导了置于饱和土体中的圆柱形孔洞瞬态动力响应解答的一般解析表达式，并将其与经典弹性动力学中圆柱形空腔问题的解答作了有价值的比较，文末利用一种十分有效的数值反变换方法给出了有意义的算例。本文为进一步分析岩土工程、地震工程中隧道、管道等地下结构的动力响应提供了有效途径，具有理论与应用价值。     

Remote detection of derailment of a wagon of a freight train: theory and experiment

Summary The paper discusses the possibility to detect derailment of a train's wagon by measuring vibrations of the rails under the locomotive. Both theoretical and experimental studies have been carried out, followed by a comparison of their results. For the theoretical modelling of the railway track, a Timoshenko beam resting on discrete, equidistantly spaced supports is used. The steady-state response of the beam to a load that either uniformly moves along the beam or uniformly `jumps' from support to next support is investigated at a point, which remains at a fixed distance from the moving load. The load that moves along the beam is used to model the `normal motion' of a train's wheelset, whereas the `jumping' load is employed to model the action of a derailed wheelset. It is shown that the effect of the derailed wheel-set consists of an amplification of the rail's response in the frequency band that surrounds the natural frequency of the sleeper's vibrations. This theoretical prediction is confirmed experimentally. A method of processing the measured data is proposed that allows for stable detection of the derailment. A maximum distance between the locomotive and the derailed wagon is estimated, at which the detection is possible.     

Dynamic analysis to infinite beam under a moving line load with uniform velocity

I.IntroductionAninfinitebeamonelasticfoundationnotonlycanbelookedonasdynamicmodelforaSuspensionbridgeoratensiondiagonalbridgel']butalsocanbeusedindynamicsanalysistoarailtrack,therefore,dynamicresponseofinfinitebeamundermovillgloadhasbecomethefocusofdiscussioninpastseveraldecades.TheproblemalsohasbeeninvestigatedbyTimoshenko12j,Frybal'],Steelel'],Lee15],etal.Wefind,however,thatallofthestudiesonthissubjectonlydiscussedmovingpointloadproblem.Actually,eitherautomobileloadoratrainloadisalinedist…