半无限大体广义电磁热弹耦合的二维问题

基于Lord和Shulman广义热弹性理论,研究了热、电可导的半无限大体电磁热弹耦合的二维问题。半无限大体受热和外加恒定磁场的作用,文中建立了电磁热弹性耦合的控制方程,利用正则模态法求解得到了所考虑物理量的解析解,并用图形反映了各物理量的分布规律,从分布图上可以看出,介质中出现了电磁热弹耦合效应,各物理量的非零值仅在一个有限的区域内。     

无限长圆柱体中广义电磁热弹耦合问题研究

基于L-S广义热弹性理论,研究了处于磁场中无限长理想圆柱导体在边界受热冲击作用时的电磁热弹耦合问题.建立了广义电磁热弹耦合的有限元方程,为避免积分变换方法求解带来的精度丟失.采用将有限元方程直接在时间域求解的方法,得到了圆柱体中的温度、位移、应力、感应磁场和感应电场的分布规律,反映了热的波动性及电磁热弹的耦合效应.结果表明,将有限元方程直接在时间域求解,可以获得各物理量的准确分布.得到温度在热波波前处的阶跃,准确地反应热波的波动效应.     

直接有限元法求解广义磁热弹二维旋转问题

为了验证直接有限元法求解广义磁热弹耦合旋转问题的有效性及准确性,该文基于Lord和Shulman(L-S)广义热弹性理论,采用直接有限元方法,求解了置于磁场中的旋转半无限大体受热冲击作用的动态响应问题.文中给出了L-S型广义磁热弹耦合旋转问题的控制方程,建立了L-S型广义磁热弹旋转问题的虚位移原理,推导得到了相应的有限元方程.通过求解有限元方程,得到了半无限大体中无量纲温度、无量纲位移、无量纲应力及无量纲磁场的分布规律,从温度分布图上可以清晰地观察到热波波前的特有属性,即热波波前处存在明显的温度突变.同时,由于旋转效应,位移、应力、感应磁场的幅值有不同程度的降低,而旋转对温度几乎没有影响.结果表明,采用直接有限元法求解L-S型广义磁热弹性耦合的二维旋转问题是十分有效和准确的.     

半无限长压电杆的瞬态热冲击问题

采用具有一个热松弛时间的L-S广义热弹性理论,研究了一维半无限长压电杆在一端受到热冲击时的边值问题.借助拉普拉斯正、反变换技术,在所考虑时间非常短的情况下,对问题进行了求解,得到了压电杆上的位移、压力及温度分布的近似解析解,发现应力及温度分布中分别存在两个阶跃点,并给出了算例.     

一维半无限压电杆的广义的热冲击问题

采用具有两个热松驰时间的G－L广义热弹性理论，研究了一维无限无限长杆在其端部受到热冲击时的边值问题，借助于拉普拉斯正、反变换技术，在所考虑时间非常短的情况下，对问题进行了求解。得到了位移及温度分布的近似妥析角，发现位移及温度分布中分别存在两上阶跃点，并通过数值计算，把温度的分布规律用图形反映了出来，从温度的分布图上可以看出，当任何x的值大于第二个阶跃点的位置值时，温度值都是零，也即在当前所绘定的时刻，热以波的形式沿压电杆仅传播到第二阶跃点的位置，而在第二个阶跃点之后，压电杆上的温度分布保持初始温度；定不同时刻，热波波前的位置也将相应的在压电杆上移动，也即热波波前在压电杆上的位置随考虑时刻不同而不同，这与经典的热传导是完全不同的，它说明热是以波的形式以有限的速度，而不是以无限的速度在介质中进行传播的。     

拉伸杆的弹粘塑性解

本文分析了弹粘塑性拉杆的蠕变特性与松弛特性．     

不同理论下广义压电热弹性问题的有限元求解

基于G-L和L-S广义压电热弹性理论研究了无限大厚压电板在上下表面受到条带状热冲击时的广义压电热弹性问题。在时间非常短的情况下，为避免积分变换求解带来的精度丢失，采用有限元方法对问题在时间域进行直接求解，获得压电板在热冲击作用下的温度、位移、应力及电势等，并将结果与经典压电热弹性理论进行比较。结果表明，直接求解方法可以准确描述热在介质中以有限的速度传播。     

激光脉冲加热的二维广义热弹性问题研究

基于L-S广义热弹性理论,研究了半无限大板局部受到激光脉冲加热时的广义热弹性问题.为避免常规积分变换方法求解带来的精度丢失,采用有限元法直接在时间域进行求解,得到了激光脉冲加热时板中的温度、位移及应力的变化规律.结果表明,直接求解方法可以准确描述热在介质中以有限的速度传播,同时发现,激光脉冲加热过后,结构的最高温度随着时间的推移逐渐降低,且最高温度的位置总在热波波前附近,此处的应力也明显高于其他区域.     

饱和多孔黏弹地基热-水-力耦合动力响应分析

天然土体由于沉积条件和应力状态不同, 往往会表现出一定的流变性. 本文研究地基上表面受外载荷作用时, 渗透系数和孔隙率变化对饱和多孔黏弹性地基热-水-力耦合动力响应问题的影响. 基于Biot波动方程、达西定律和Lord-Shulman广义热弹性理论, 并引入了考虑黏弹性松弛时间因子的Kelvin-Voigt黏弹性模型研究地基上表面受热/力源作用时, 孔隙率和渗透系数变化对均质各向同性饱和多孔黏弹性地基中所考虑的各无量纲量的影响. 根据不同的边界条件采用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度的解析表达式, 结合算例分析了不同变量对各物理量的影响. 正则模态法是一种加权残差法, 可不经正、反积分变换将方程快速解耦并消除数值反变换的局限性. 结果表明: 无论何种载荷作用时, 载荷频率变化对所有考虑的物理量均有明显的影响; 孔隙率和渗透系数均对无量纲超孔隙水压力有明显的影响, 当仅考虑热载荷作用时, 孔隙率和渗透系数变化对无量纲温度均无影响. 正则模态法可广泛应用于岩土工程领域, 尤其适用于商业建筑、高速铁路和公路能源基础的热、力学特性研究中. 该研究结果可为工程施工奠定一定的理论基础, 具有一定的指导性意义.      

磁弹性、热磁弹性理论及其应用

介绍了磁弹性、热磁弹性的基本内容,发展简史,基本方程,理论研究,实际应用研究及其未来应用前景．      

An Edge Crack Problem in a Semi-Infinite Plane Subjected to Concentrated Forces

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Helical Outflow through a Circular Hole in the Bottom of a Semi-Infinite Cylinder (Modification of a Slezkin Problem)

The steady axisymmetric helical flow of an incompressible ideal fluid in a semi-infinite cylinder due to the presence of a circular hole in its bottom is analyzed. At an infinite distance from the bottom, in contrast to the similar problem considered by N. A. Slezkin, constant axial and angular components of the quasi-rigid rotation are maintained and the hole-induced flow is uniformly helical in the Zhukovsky sense, that is, the vorticity vector of the absolute motion is collinear to the relative velocity. In the coordinate system rotating with the fluid, this flow can be represented as the superposition of a straight-line translational flow in the direction of the bottom and a uniformly helical Gromeka-Beltrami flow. The problem is solved using the generalized stream function. The limiting cases of a helical sink in the bottom of a semi-infinite cylinder and helical flow out of a half-space through a circular hole on the boundary are considered. The results are compared with those for potential flow.     

A Generalized Piezoelectric Bernoulli–Navier Anisotropic Rod Model

We apply the asymptotic analysis procedure to the three-dimensional static equations of piezoelectricity, for a linear nonhomogeneous anisotropic thin rod. We prove the weak convergence of the rod mechanical displacement vectors and the rod electric potentials, when the diameter of the rod cross-section tends to zero. This weak limit is the solution of a new piezoelectric anisotropic nonhomogeneous rod model, which is a system of coupled equations, with generalized Bernoulli–Navier equilibrium equations and reduced Maxwell–Gauss equations.     

Generalized Solutions of the Capillary Problem

It was pointed out by Finn [2] that the capillary problem in zero gravity has not always a classical (smooth) solution in the case that the bounded domain Ω⊂ℝ² contains cusps or corners. Here, ω denotes the cross section of a given cylinder, in which a liquid is contained. If special energy terms could become infinite the variational formulation is not free of limitations as well. Therefore, the concept of generalized solutions, which can be traced back to Miranda [11], has been developed and could be a way out. We want to prove an existence result for such solutions under very weak preconditions. The proof is closely related to Giusti's paper [6], but we do not require full smoothness of the boundary. The major new difficulty is that we also want to consider domains with non-Lipschitz boundary. This excludes the application of some theorems. On the other hand, we use special geometric conditions in ℝ² and consequently, the proof cannot easily be generalized to a higher dimension. Furthermore, we construct some generalized solutions explicitly.     

Problem of Pulse Start-up of a Gas Bearing in a Generalized Formulation

The time-dependent motion in the lubricating layer of a gas bearing is analyzed on the basis of the compressible boundary layer equations with allowance for the inertial effects and the transverse temperature drop. After introducing certain assumptions concerning the order of the main dimensionless parameters, approximate expressions for the velocity and temperature are derived. As a result, the problem reduces to the determination of the pressure as a function of the space coordinate and time.     

Behavior of a Semi-Infinite Ice Cover Under a Uniformly Moving Load

This paper consideres the behavior of a semi-infinite ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a load moving with constant velocity along the edge of the cover at some distance from it. The ice cover is modeled by a thin elastic plate of constant thickness. In a moving coordinate system, the deflection of the plate is assumed to be steady. An analytic solution of the problem is obtained using the Wiener–Hopf technique. The wave forces, the deflection of the plate, and the elevation of the free surface of the fluid at different velocities of the load are investigated.     

杆的差分离散系统一个新的模态反问题

本文研究杆的差分离散系统一个新的模态反问题,所考虑的杆件是同一种均匀材料构成的,但横截面积不恒定.首先,我们给出了变截面杆的纵向自由振动方程,采用分离变量法,得到了模态方程.然后,在最一般的边界条件,即两端弹性支承的边界条件下,采用二阶中心差分公式,导出了杆的差分离散模型.结果表明,所得到的系统属于标准雅可比系统.只对...     

The Generalized Membrane Problem for Linearly Elastic Shells with Hyperbolic or Parabolic-Middle Surface

We consider a linearly elastic shell with a hyperbolic, or parabolic, middle surface, clamped along a large enough portion of its lateral face and subjected to body forces. We then show that the two-dimensional limit model found by the asymptotic analysis from the three-dimensional shell problem is the “generalized membrane” shell model, according to the terminology introduced by P.G. Ciarlet and V. Lods. We also identify the functional space where this model is well posed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Analysis of Constitutive Assumptions for the Strain Energy of a Generalized Elastic Membrane in a Nonlinear Contact Problem

For very thin shell-like structures it is common to ignore bending effects and model the structure using simple membrane theory. However, since the thickness of the membrane is not modeled explicitly in simple membrane theory it is not possible to use the three-dimensional strain energy function directly. Approximations must be introduced like the assumptions of: no thickness changes, generalized plane stress or incompressibility. In contrast, the theory of a Cosserat generalized membrane uses the three-dimensional strain energy function directly, it includes both thickness changes and shear deformation and it allows contact conditions to be formulated on the interface of the membrane with another body instead of on the middle surface of the membrane. A specific nonlinear contact problem is used to study these effects and comparison is made with solutions of a hierarchy of theories which include different levels of deformation through the thickness of the membrane and different formulations of the contact conditions. The results indicate that within the context of a simple membrane the assumption of generalized plane stress is best for this problem and that a generalized contact condition extends the range validity of the simple membrane solution to thicker membranes.