Analysis of Newton’s Method to Compute Travelling Waves in Discrete Media

We present a variant of Newton’s method for computing travelling wave solutions to scalar bistable lattice differential equations. We prove that the method converges to a solution, obtain existence and uniqueness of solutions to such equations with a small second order term and study the limiting behaviour of such solutions as this second order term tends to zero. The robustness of the algorithm will be discussed using numerical examples. These results will also be used to illustrate phenomena like propagation failure, which are encountered when studying lattice differential equations. We finish by discussing the broad application range of the method and illustrate that higher dimensional systems exhibit richer behaviour than their scalar counterparts.     

Integration of an Equilibrium System in an Enhanced Theory of Bending of Elastic Plates

The complete integral of the system of partial differential equations governing the equilibrium bending of elastic plates with transverse shear deformation and transverse normal strain is constructed by means of complex variable methods. The process helps to elucidate the physical meaning of certain analytic constraints imposed on the asymptotic behavior of the solutions and shows that in the case of an infinite plate, any analytic solution has finite energy if and only if the bending and twisting moments, the transverse shear force, the displacements in vertical planes, and two other characteristic quantities vanish at infinity. An example is discussed to illustrate the theory.     

Action of a Periodic Load on an Elastic Floating Plate

The problem of the behavior of an elastic floating plate in the form of a strip under the action of a periodic surface load is solved using the Wiener-Hopf technique. The shortwave approximation is found in explicit form. The effect of the frequency and nature of the acting load on the vibration amplitudes of the fluid and the plate is investigated numerically. It is found that for certain loads no waves propagate in the fluid and the vibrations of the plate are localized in the neighborhood of the acting load. Conditions under which local vibration can be realized are found.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 132–146.Original Russian Text Copyright © 2005 by Tkacheva.     

Materials Sensitive to the Type of Process

Several effects associated with the sensitivity of materials to various processes have been long known. Among such processes are: tension or compression; torsion in different directions; various stress combinations, etc. (sensitivity to the type of loading); stretching or compression, etc. (sensitivity to the type of deformation); creep or relaxation, processes with different strain rates, etc. (sensitivity to the type of rheological processes). There are many successful propositions as to how to model these types of sensitivity for every particular case. This presentation proposes a new approach to generalize all these events using a unified model. The model is based on introducing an extended space of events, including stress and strain subspaces, and time scale (or the well-known internal time scale). Some subspaces with single-type processes ought to be identified. In every single-type process, a subspace of one material model is preferable. Of special importance is the transition from one subspace to another. Under various experimentally examined conditions, it is possible to introduce some simplified quadratic surfaces of constant stress and strain states (measured from their intensities at fixed time points). This approach is applied to various characteristic cases. The important issue of solving the system of equations that describes the behavior of a material in case of complex multi-type processes is discussed     

具有规则表面织构的超高分子量聚乙烯髋臼表面温度分析

就人工关节中广泛使用的超高分子量聚乙烯(UHMWPE)髋臼在运行中的瞬态表面温度场进行了理论计算,与理想光滑表面对比考察了微球表面织构对接触压力分布的影响及其引起的表面温度变化.结果表明,基于光滑表面计算得到的髋臼表面温度偏低,而基于规则织构表面计算得到的温度与文献值接近;髋臼表面温度随摩擦系数和载荷增加而升高,随关节摆动而呈现周期性变化.     

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.     

The reference shrinkage curve of clay soil

The objective of this work is to develop and validate a model that predicts the reference soil shrinkage curve, that is one without crack volume contribution, as a necessary preliminary step in future estimation of soil crack volume from soil shrinkage data. Current soil shrinkage models are based on the approximation of soil shrinkage data by some a priori taken mathematical expressions and justified by the fitting of their parameters to the data. However, the crack volume entering the data is not single valued and depends on shrinkage conditions. Unlike that the reference shrinkage curve is single valued. For soils with sufficiently high clay content when there are no large pores (lacunar pores) inside the intra-aggregate clay, the reference shrinkage curve is derived from the assumption of the rigid superficial (interface) layer of aggregates with changed pore-size range and distribution compared with the intra-aggregate matrix. This consideration is based on accounting for contributions of the interface aggregate layer and intra-aggregate matrix to the soil volume and water content during shrinkage. The reference shrinkage curve is predicted by eight fundamental physical immediately measured parameters of (i) the intra-aggregate matrix (including clay content); (ii) the aggregate structure; and (iii) the mean silt-sand grain size or mean interface layer thickness. The model was validated using the data for eight soils. In addition to the major potential application for estimating a soil crack volume, the model explains differences between the observed shrinkage curves of soil and pure clay, and it can have other numerous applications.     

飞机风挡结构抗鸟撞一体化设计技术研究

结合大型非线性有限元分析软件，实践了飞机风挡结构由初步设计、数值仿真以及实验验证的一体化设计过程，建立了适于风挡结构材料的非线性黏弹性本构计算接口程序，对合理选取单元类型、材料模型、边界条件影响以及试验设计等工作细节进行了深入研究，通过实验与仿真计算结果的对比，验证了数值仿真计算模型的精度．为飞机风挡的抗鸟撞结构设计-数值仿真-实验验证一体化技术提供了支持论证．     

Transformation of a breaking wave at a drop of a channel bottom

This paper gives results of an experimental study of incident and reflected waves of the bore type in the neighborhood of a sharp change in the channel bed level. It is shown that under conditions typical of accidents at ship locks, the wave height can reach 8 m.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 115–121, March–April, 2005.     

残余应力对压力容器破坏模式的影响分析

破前漏(简称LBB)是压力容器、核电站设备结构设计与评价中的一个重要准则.表面裂纹准静态扩展的几何形貌变化规律的预测是破前漏(LBB)评判十分重要的课题之一.本文对特定焊接残余应力场加载作用下,含三维表面裂纹的压力容器模型,用有限元软件(ABAQUS)进行了表面裂纹准静态扩展模拟计算,得到在此残余应力场作用下应力强度因子沿裂纹前缘的分布规律.结合外载引起的应力强度因子,就可以判别裂纹的扩展形貌,从而判断结构是否满足LBB要求.