Elastic constants of monotropic plastic foams. 2. Deformation parallel to foam rise direction. Numerical calculations

In order to perform numerical calculations of the elastic constants of monotropic plastic foams with a pronounced strut-like structure, a package of computing programs has been developed. Numerical values of the elastic constants were determined using the Simpson method for the calculation of triple averaging integrals and stepwise unconditional minimization of the one-argument potential energy function. The parameters of the numerical calculation process providing acceptable accuracy of the results were evaluated. Dimensions of the structural elements in the model of isotropic plastic foams were determined and analyzed.Institute of Polymer Mechanics, Riga, LV-1006, Latvia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 2, pp. 163–172, March–April, 1998.     

Elastic constants of monotropic plastic foams. 1. Deformation parallel to foam rise direction. A mathematical model

A mathematical model of the deformative properties and structure of lightweight, monotropic (or isotropic in the limiting case) plastic foams with a pronounced strut-like structure has been elaborated in the linear theory of deformation. A selection of five independent elastic constants is described. For the integral characterization of the deformative properties of plastic foams as micrononhomogeneous composite materials, the elastic constants are introduced as the effective constants. In order to describe the plastic foam structure, a local model consisting of two parts is proposed, i.e., a model of a continuous medium for the calculation of stresses and a local structure model. Considering deformation parallel to the foam rise direction when the semiaxes hypothesis is assumed, the Young modulus and Poisson's ratio are determined.Institute of Polymer Mechanics. Translated from Mekhanika Kompozitnykh Materialov, Vol. 33, No. 6, pp. 719–733, November–December, 1997.     

Dynamical and Static Analysis of the Deformation of a Fluid-Filled, Piecewise-Homogeneous Elastic Shell

The dynamical problem of the distribution of a pressure wave initiated at a certain distance from a junction of fluid-filled elastic shells having different properties is investigated. The static problem of two connected, empty (without the fluid) elastic shells having different properties is investigated as a special case of the dynamical problem and as a first step in the investigation of the stated problem. The results are subjected to a comparative analysis, and estimates are obtained for the solution of the dynamical problem in contrast with the static version.     

基于曲梁弹性理论的弯曲覆岩变形及应力分析

引入适用于极坐标下曲梁的位移函数,通过理论分析得出用位移函数表示的曲梁控制方程和位移分量、应力分量.在此基础上,采用差分原理给出曲梁控制方程、位移分量和应力分量的差分代数方程.最后,采用数值计算方法,分析了煤层开采后弯曲覆岩的位移和应力分布特征,结果表明:1)煤层开采后弯曲覆岩产生下沉变形;弯曲岩层环向位移既有拉伸也有压缩.2)离开切眼不远处径向应力将达到峰值,径向应力由内边界向外逐渐增大;工作面后方不远处环向应力将达到峰值,环向应力较容易引起压缩破断;离开切眼不远处剪应力将达到峰值,对于小角度截面上的剪应力由内边界向外逐渐增大.研究结果为煤矿工程提供了科学依据与参考.     

Some results related to the toughness of 3-domination critical graphs

A graph G is said to be k-γ-critical if the size of any minimum dominating set of vertices is k, but if any edge is added to G the resulting graph can be dominated with k−1 vertices. The structure of k-γ-critical graphs remains far from completely understood, even in the special case when the domination number γ=3. In a 1983 paper, Sumner and Blitch proved a theorem which may regarded as a result related to the toughness of 3-γ-critical graphs which says that if S is any vertex cutset of such a graph, then G−S has at most |S|+1 components. In the present paper, we improve and extend this result considerably.     

New results in the theory of multivalued mappings. II. Analysis and applications

This is the second part of a survey by Yu. G. Borisovich, B. D. Gel'man, A. D. Myshkins, and V. V. Obukhovskii on new results in the field of analysis of multivalued mappings and their applications during the 1980's.Translated from Itogi Nauki i Tekhniki, Seriya Matematicheskii Analiz, Vol. 29, pp. 107–159, 1991.     

非线性尺规近似法在圆杆颈缩局部有限变形分析中的应用

形变局部化和不稳定的研究是当前力学问题的一个热点,其中最典型的问题是圆杆拉伸颈缩和滑移带的塑性分析。传统的微小变形弹塑性力学不能彻底解决此问题。本文采用以S(应变)-R(转动)分解定理为基础的非线性尺规数值计算法,并应用计算机模拟优化技术求出圆杆拉伸轴对称塑性有限变形的局部应变分布与发展形态。     

A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Integration of the subsurface flow equation by finite elements (FE) in space and finite differences (FD) in time requires the repeated solution to sparse symmetric positive definite systems of linear equations. Iterative techniques based on preconditioned conjugate gradients (PCG) are one of the most attractive tool to solve the problem on sequential computers. A present challenge is to make PCG attractive in a parallel computing environment as well. To this aim a key factor is the development of an efficient parallel preconditioner. FSAI (factorized sparse approximate inverse) and enlarged FSAI relying on the approximate inverse of the coefficient matrix appears to be a most promising parallel preconditioner. In the present paper PCG using FSAI, diagonal and pARMS (parallel algebraic recursive multilevel solvers) preconditioners is implemented on the IBM SP4/512 and CLX/768 supercomputers with up to 32 processors to solve underground flow problems of a large size. The results show that FSAI may allow for a parallel relative efficiency larger than 50% on the largest problems with p=32 processors. Moreover, FSAI turns out to be significantly less expensive and more robust than pARMS. Finally, it is shown that for p in the upper range may be much improved if PCG–FSAI is implemented on CLX.     

Global strong solutions to 3-D Navier-Stokes system with strong dissipation in one direction Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

We consider three-dimensional incompressible Navier-Stokes equations(NS) with different viscous coefficients in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared with the initial data, we prove the global well-posedness of this system. In fact, we obtain the existence of a global strong solution to(NS) when the initial data verifies an anisotropic smallness condition which takes into account the different roles of the horizontal and vertical viscosity.     

Application of the reduced concentration principle to filled polymers 3. Polyolefins

The reduced concentration principle is used to construct generalized modulus of elasticity vs filler content dependences for filled polyolefins that are invariant relative to the nature and surface of the filler. If the change in crystallinity associated with filling is taken into account, the master curve for filled low-density polyethylene can be reduced to the Smallwood-Guth equation.     

Interpretation of the Evolution of the Homogeneous Markov System (or,equivalently, of the Embedded Markov Chain) as the Deformation of a Viscoelastic Medium. The 3-D Case

Every attainable structure of a continuous time homogeneous Markov chain (HMC) with n states, or of a closed Markov system with an embedded HMC with n states, or more generally of a Markov system driven by an HMC, is considered as a point-particle of ? ⁿ . Then, the motion of the attainable structure corresponds to the motion of the respective point-particle in ? ⁿ . Under the assumption that “the motion of every particle at every time point is due to the interaction with its surroundings”, ? ⁿ (and equivalently the set of the accosiated attainable structures of the homogeneous Markov system (HMS), or alternatively of the underlying embedded HMC) becomes a continuum. Thus, the evolution of the set of the attainable structures corresponds to the motion of the continuum. In this paper it is shown that the evolution of a three-dimensional HMS (n = 3) or simply of an HMC, can be interpreted through the evolution of a two-dimensional isotropic viscoelastic medium.     

Development of Engineering Approaches to the Study of Interference Wave Fields Excited in Packets of Thin Elastic Layers. II (Numerical Methods for Evaluating Wave Fields. A Brief Review of the Results Obtained)

An algorithmic-analytical approach to the quantitative study of wave fields in thin-layered elastic media is considered. The basic ideas of a numerical algorithm are stated. Examples of the computation of wave fields are given. Bibliography: 1 title.     

An Econometric Approach to Short-Run Analysis of the U.K. Economy, 1955-66

The structural approach to economic forecasting differs from familiar models based on the classical analysis of time series in that it requires the specification and estimation of the inter-relationships that are taken to represent economic structure. The first part of the paper deals briefly and rapidly with some of the problems encountered in specifying and estimating such structural models. The second part deals with the applications of such models and their implications for forecasting and policy analysis. These sections are intended to be fairly allusive and preparatory to the main body of the paper which discusses a specific example of a simple econometric model of the U.K. economy constructed at the London Business School. The model is described in terms of its structural relationships, and the results of some simulation work are presented. The paper concludes with some general evaluation of the approach in the light of the specific illustration discussed.