The normal contact of rough surfaces with fine discretization

Summary The numerical treatment of a 3-d frictionless normal contact of rough bodies made of a linear–elastic, isotropic material is considered. First, the governing equations and their discretized forms are presented. Due to the order of the problem, the computation time rapidly increases with the grid refinement. Therefore, common computer programs have to be limited to 50×50 contact points. Several numerical techniques (multigrid, iterative solver, distributive relaxation) are used. Cell-centered grid transformation is applied and grid operators have been established for this purpose. In order to handle upto 1000 × 1000 cells the program CON3D has been developed.     

1／2亚谐共振──主参数共振情况下非线性振动系统的余维2退化分叉

本文应用Normal Form理论和退化向量场的普适开折理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,用Melnikov方法讨论了全局分叉的存在性.     

一种求解层合圆柱壳的杂交应力单元

根据修正的余能原理，推导出一种求解复合材料层合圆柱壳的杂交应力单元。取用六面体等参单元，此单元反映了各层材料性质不同及应力分布沿整个厚度不连续现象，同时计入横向剪切变形和法向挤压变形，适用于厚层壳体。文章通过实例说明此单元能准确求出各层内的应力值，实用价值高。     

A connection between linear normal modes and lines of curvature on the potential surface

For the N-degree-of-freedom of linear conservative vibratory systems, the corresponding potential functions can be viewed as N-hypersurfaces in (N + 1)-dimensional space. In this paper, a connection between the geometrical properties (principal curvatures, curvature lines) of potential surfaces and the vibratory characteristics (natural frequencies, linear modes) of the system is built. It is proved that the linear normal modes are exactly the projections of the lines of curvature on the potential surface onto the configuration space with metric m_ij (the mass-matrix); and that the squared natural frequencies are exactly the principal curvatures, at the origin of the configuration space, of the potential surface.     

非线性动力系统的规范形和余维3退化分叉

本文里我们利用矩阵表示法计算了具有Z_(2~-)对称性时非线性动力系统的高阶规范形,求出了余维2退化和余维3退化情况下相应规范形的普适开折。最后利用所得到的规范形和普适开折讨论了非线性动力系统的余维3退化分叉。     

NOTES ON A STUDY OF VECTOR BUNDLE DYNAMICAL SYSTEMS(Ⅱ)──PART 1

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Quasistatic Viscoelastic Contact with Normal Compliance and Friction

We prove the existence of a unique weak solution to the quasistatic problem of frictional contact between a deformable body and a rigid foundation. The material is assumed to have nonlinear viscoelastic behavior. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We establish the continuous dependence of the solution on the normal compliance function. Moreover, we prove the existence of a unique solution to the problem of sliding contact with wear. This revised version was published online in August 2006 with corrections to the Cover Date.     

关于具有激波的流动的稳定性

<正> 1、引言 流体运动总是同时受动力学和热力学规律的约制,通常处理流动问题时这两方面的考虑也总是交织在一起,例如,为了定义描述流动现象的诸流动变量,首先要假定每个流体质点微团是处于热力学平衡态,即假定流动系统满足“局域热平衡”条件。这样才可以定义各“点”的压力、密度、熵等变量。由于流动系统同时又是一个热力学系统,因此它的     

Gravitational Stability of the Interface in Water Over Steam Geothermal Reservoirs

Stability of a geothermal system is considered in a case when the water layer lies over the layer of superheated vapor in a stratum having relatively low permeability. This stratum locates between two parallel high permeable layers. Under the assumption of smallness of advective energy transfer as compared with the conductive one, the stationary distribution of the characteristics in the stratum with an interface of phase transition is obtained. The interface separates the domains occupied by water and vapor. Investigation of normal stability of the interface shows, that stable configurations in the geothermal system under consideration exist within the range of permeability values bounded by k 0.6 × 10^–15 m² from above. The most unstable configurations occur to be the quiescent states when the permeability exceeds a certain threshold. A sufficiently high value of permeability, satisfying the criterion of smallness of the advective energy transfer as compared with the conductive one makes it possible to explain the existence of a wide class of stable natural geothermal reservoirs, where the vapor layer underlies the water one.     

多自由度内共振系统非线性模态的分岔特性

利用多尺度法构造了一个立方非线性1:3内共振系统的内共振非线性模态(NonlinearNormal Modes associated with internal resonance)．研究表明,内共振非线性系统除存在单模态运动外还存在耦合模态运动．耦合内共振模态具有分岔特性．利用奇异性理论对模态分岔方程进行分析发现此类系统的模态存在叉形点分岔和滞后点分岔这两种典型的分岔模式．