Variational Problem on Equilibrium of an Elastic Medium Located in Elastic Shell

The global solvability of the problem about equilibrium of an elastic medium located in an elastic shell is established by variational methods. In the case of one-parametric force field, the bifurcation problem is studied. As is shown, the standard necessary condition for bifurcation is also sufficient for the problem under consideration. Bibliography: 7 titles.     

连续介质中杆件系统的振动问题

弹性连续介质中杆件系统的振动问题,是工程中经常遇到的,这是弹性动力学和结构动力学的混合求解问题。按照一般的方法进行求解,似乎有很多困难,且很复杂。本文采用Lagrange乘子法,给出了这种类型平面问题的广义泛函。并通过实例说明本文方法的应用。     

平面P波在弹性介质和非饱和多孔弹性介质分界面上的传播

使用线性粘滞的多孔弹性介质模型,解决在弹性介质和非饱和多孔弹性介质分界面上平面P波的反射与透射问题,这里的非饱和多孔介质中固体骨架被两种相互耦合的流体（液体和气体）所充满．通过势函数的方法得到了振幅反射系数与振幅透射系数．然后推导得到入射波与反射波、透射波之间能量转换情况．研究发现:用振幅比和能量比所表示的反射系数与透射系数是与入射角度、饱和度、入射频率以及上下层介质的弹性常数有关的方程式．数值计算通过图形的形式表达出来,而且入射角度、频率及饱和度对振幅和能量的反射与透射系数的影响分别进行了讨论．证明了在整个波的传播过程中分界处并没有发生能量的耗散．     

Motion of a Force Source over an Elastic Surface

The motion of a variable point force P(t) over the free surface of an elastic half-space is investigated with a view toward studying wave processes in an elastic medium. Special attention is given to the determination of surface wavefronts, because the detection of the latter from seismogram data can be utilized to locate the position of a source in space and time. This type of planar problem has been investigated previously, for example, in [1], but the analytical solutions of the problem of a stationary source moving with a constant velocity have been obtained only in the limit t without regard for the transient process of wave propagation.     

Scattering on a Small Inhomogeneity in an Elastic Medium

Problems on the diffraction of elastic plane waves (transverse and longitudinal) scattered on a cylinder are investigated. The radius a of the cylinder is small enough ( , where is the wave number). The waves of horizontal polarization (SH waves) are scattered similarly to the electromagnetic wave of the respective polarization. It is proved that a small inhomogeneity radiates as a point source, with its amplitude proportional to the difference of the Lamé parameters and and to the area of a cross section of the inhomogeneity. The scattering of a plane wave of vertical polarization is subject to a more complicated law of radiation, because of the vector nature of the problem, and the respective components of the displacement vector are represented in terms of the scalar and vector potentials. However, the scattering of the wave field on the small inhomogeneity has qualitatively the same asymptotic behavior as in the case of the SH wave. Bibliography: 4 titles.     

The Basic Mixed Problem for an Anisotropic Elastic Body

The mixed boundary value problem is considered for an anisotropic elastic body under the condition that a boundary value of the displacement vector is given on some part of the boundary and a boundary value of the generalized stress vector on the remainder. Using the potential method and the theory of singular integral equations with discontinuous coefficients, the existence of a solution of the mixed boundary value problem is proved.     

The Reduced Basis Method for an Elastic Buckling Problem

In this work, we apply the Reduced Basis (RB) Method to the field of nonlinear elasticity. In this first stage of research, we analyze a buckling problem for a compressed 2D column: Here, the trivial linear solution is computed for an arbitrary load; the critical load, marking the transition to nonlinearity, is then identified through an eigenvalue problem. The linear problem satisfies the Lax-Milgram conditions, allowing the implementation of both a Successive Constraint Method for an inexpensive lower bound of the coercivity constant and of a rigorous and efficient a posteriori error estimator for the RB approximation. Even though only a non-rigorous estimator is available for the buckling problem, the actual RB approximation of the output is more than satisfactory, and the gain in computational efficiency significant. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Motion of a Heavy Cylinder over the Surface of an Anisotropic Elastic Solid

The response of an anisotropic elastic half-space to a heavycylinder moving steadily over its surface is examined. The analysisholds for the most general anisotropy in which no symmetry elementsof the material are assumed.     

A Time-dependent Interaction Problem Between an Electromagnetic Field and an Elastic Body

This paper considers the scattering of a time-dependent electromagnetic plane wave by a bounded elastic body.An appropriate decomposition of the coupling interface conditions is proposed according to the Voigt’s model between the electromagnetic and elastic medium.The original unbounded scattering problem is equivalently reduced into an initial-boundary value problem in a bounded domain by introducing an exact transparent boundary condition(TBC)on a sufficiently large sphere.Making use of the Lax-Milgram lemma,the abstract inversion theorem of Laplace transform and the energy method,we verify the well-posedness and stability for the reduced problem.Moreover,a priori estimates are established for the electromagnetic field and elastic displacement by taking special test functions directly in the time domain variational formulation.     

Wave Propagation in an Elastic Medium Intersected by Systems of Parallel Fractures

An elastic anisotropic medium intersected by systems of parallel fractures is investigated. Every fracture is considered as a plane boundary with jumps of displacements and stresses, and these jumps are linear functions of displacements and stresses averaged on the boundary. For this medium, an effective model is constructed by the method of matrix averaging. The equations of this model describe wave propagation in the given medium and are more complicated than the equations of elasticity theory. In particular cases, the equations obtained are converted to the equations of elastic media. On the basis of the equations of the effective model, expressions for the densities of the kinetic and potential energies are derived, and conditions of absoption in the medium are established. Bibliography: 15 titles.     

一种改进边界元法在弹性扭转问题中的应用

本文用一种改进边界元法分析与计算了椭圆截面等直杆的扭转问题.并与边界元法的解进行比较,其结果极为符合.然而,改进边界元法较边界元法所需要的数据量少得多,计算时间也将大大减少了.因此,本文方法对求解Poisson方程问题是一种经济而行之有效的数值计算方法.     

Brownian Motion and the Dirichlet Problem at Infinity on Two-dimensional Cartan-Hadamard Manifolds

After recalling the Dirichlet problem at infinity on a Cartan-Hadamard manifold, we describe what is known under various curvature assumptions and the difference between the two-dimensional and the higher-dimensional cases. We discuss the probabilistic formulation of the problem in terms of the asymptotic behavior of the angular component of Brownian motion. We then introduce a new (and appealing) probabilistic approach that allows us to prove that the Dirichlet problem at infinity on a two-dimensional Cartan-Hadamard manifold is solvable under the curvature condition K?≤?(1?+?ε)/(r ² logr) outside of a compact set, for some ε?>?0, in polar coordinates around some pole. This condition on the curvature is sharp, and improves upon the previously known case of quadratic curvature decay. Finally, we briefly discuss the issues which arise in trying to extend this method to higher dimensions.     

Front Motion in a Problem with Weak Advection in the Case of a Continuous Source and a Modular-Type Source

Differential Equations - We obtain an asymptotic approximation to a moving inner layer (front) solution of an initial–boundary value problem for a singularly perturbed parabolic...     

On the Unique Solvability of the Optimal Starting Control Problem for the Linearized Equations of Motion of a Viscoelastic Medium

Differential Equations - We study an optimization problem for the linearized evolution equations of the Oldroyd model of motion of a viscoelastic medium. The equations are given in a bounded...     

Attenuating Resonance Modes in a Cylindrical Waveguide Placed in an Elastic Medium

Interference attenuating waves traveling in a cylindrical elastic waveguide, placed in an elastic medium, are considered. The group velocity of these waves is intermediate between that of the P wave and that of the S wave; the phase velocity equals that of the P wave. The frequency of the waves is almost constant and is determined by the requirement of constructive interference. The dispersion and attenuation of these waves are described. Bibliography: 3 titles.     

带裂缝的半平面弹性基本问题

本文用复变方法讨论了半平面内含若干条任意形状裂缝时的弹性基本问题,包括各向同性和各向异性两种情况,把寻求复应力函数的问题归结为求解某种带若干待定常数的正则型奇异积分方程,证明了若适当且唯一地选择这些常数的值,该方程的解存在且唯一。     

弹性介质中正交各向异性微管的屈曲分析

已有实验表明,处于细胞质中的微管可以比自由微管承受更大的压力而不发生屈曲．基于嵌入式碳纳米管屈曲的Winkler模型,利用正交各向异性情形的Winkler模型研究了细胞质中充当细胞骨架的微管的屈曲行为．计算表明,本模型可以较好地预测嵌入弹性介质中的微管较自由微管承受更大屈曲压力这一现象,而且所得到的临界屈曲压力与微管受压屈曲的实验值吻合\．同时,所得的结果也表明周围介质与微管的相互作用可以极大地提高微管抵抗屈曲的能力,该结果很好地阐释了介质与微管相互作用从而提高微管抗屈曲压力的相互作用机制\．模拟结果表明,所给出的模型可以对嵌入弹性介质中的微管的屈曲行为进行很好地模拟．