Simulation of spallation in brittle solids

A new model of dynamic fracture for brittle materials based on Perzyna's[1] idea and Seaman's experimental results[2] is developed. Numerical simulations of metal uranium[3] spalling process in its impact tests are carried out with the model. Fair agreement between the computation and experimental data has been obtained.     

Second-order cnoidal waves at the free surface and interface of a two-fluid system

In this paper, using the PLK method and reductive perturbation method, we obtained the second approximation to cnoidal waves at the free surface and interface for the two-fluid system considered in [1]. The corresponding results in [3] and [4] may be obtained as special cases in this paper.Projects Supported by the Science Fund of the Chinese Academy of Sciences.     

A polynomial method for solving the problems for lateral instability of cantilever plates

The present article researches the problems of the lateral instability of cantilever rectangular plates under a concentrated force or a uniformly distributed load respectively.We select the polynomial(2.1)instead of the cosecant function in Ref.[1]as the flexural functions.The minimum critical load obtained here is more exact than the results obtained in Ref.[1]     

ON LIAPOUNOFF’S METHOD IN THE THEORY OF STABILITY OF LAMINAR FLUID FLOWS

In[1]Zhou extended some Liapounoff‘s theorems of the theory of stability in the case of plane laminar fluid flows.In[2]Zhou and Li investigated the eigenvalue problem and expansion theorems associated with Orr-Sommerfeld equation,and obtained some new results.In this paper,based on the results of[1]and[2]we shall prove:(1)For the linearized problem the definition of stability according to the eigenvalues of Orr-Sommerfeld equation and that according to the perturbation.energy are equivalent;(2)The method of linearization is admissible for the stability pro-blem of plane laminar fluid flows for sufficiently small initial disturbance.     

Non-equilibrium thermodynamics of heterogeneous systems and history dependent materials

A non-equilibrium thermodynamic theory due to Bree and Beevers [1] has been applied by Bree [2] to a certain class of mixtures, referred to in [2] as simple mixtures where it is found that global and local entropy inequalities can be obtained for the whole mixture, for each of its constituents or for any combination of its constituents, each of these entropy inequalities being derived from the single statement of the second law of thermodynamics adopted in [1]. The present work is primarily concerned with developing the theory further in order to include the more complex class of mixtures referred to in [2] as heterogeneous systems. In contrast with the thermodynamics of simple mixtures, it is found that for heterogeneous systems global and local entropy inequalities can be obtained only for the whole mixture and, in connection with this, it is felt that an early controversy in the subject is resolved. It is shown how the results obtained for heterogeneous systems may be used to provide a thermodynamic foundation for two methods of representing history dependent materials.     

On the driving traction acting on a surface of discontinuity within a continuum in the presence of electromagnetic fields

The notion of the driving traction of Knowles [6] is generalized to account for the interaction of a continuum with electromagnetic fields, and the expression for the generalized driving traction is reduced to that of Abeyaratne and Knowles [15] in the absence of electromagnetic fields. The admissibility condition implied by the second law of thermodynamics is discussed and the results are consistent with those obtained in [23] where a thermoelastic polarizable material undergoing a bulk phase transition is considered.     

GENERAL RANDOM FIXED POINT THEOREM AND ITS APPLICATIONS

In this paper,we obtain a general random fixed point theorem which generalizes the main results of Engle[4,7] and Bocsan[8]. The usefulness of this theorem seems to lie in the fact that unlike many random fixed point theorems obtained by using special methods[1,4,5-13] can be proved by using out general theorem (Theorem 1 and Corollaries 1 and 2). Finally,we indicate some possible applications of our results to nonlinear random integral and differential equations.     

The random choice method and the free-surface water profile after the collapse of a dam wall

The random choice (RC) method due to Glimm [1], subsequently modified by Chorin [2] and Sod [3], is applied to the shallow water equations of Stoker [4], in order to determine the free-surface profile of water, as a function of position and time, when a dam wall suddenly collapses. The numerical results obtained by this method are compared with the analytical results due to Stoker for this classical problem [5], and with numerical results obtained by a further modification of the Glimm-Chorin scheme involving a smoothing operation. The improvement brought about by the smoothing, and the generally close agreement with the exact result that is then obtained, is a feature of this modified approach.     

利用钻孔法测定残余应力问题

钻孔法是测量残余应力的一个重要方法。本文就有关文献所提供的A、B值进行分析和比较。对试验中由于贴片钻孔所造成的偏差提出了修正公式。此公式使用简便,经验算,误差在10％以内。     

层状介质中多个非共面硬币形裂纹弹性波散射问题研究

本文在[1]的基础上,利用 Hankel 积分变换,进一步研究了层状介质中多个非共面硬币形裂纹的弹性波散射问题。从所得结果来看,虽然层状介质中多个非共面硬币形裂纹的弹性波散射问题在形式上与多个非共面穿透形裂纹问题[1]有惊人的相似之处,但两者之间有着质的差异。     

Rate equations for viscoplastic materials subjected to finite strains

The constitutive equations for plasticity proposed by Voyiadjis [1984] and Voyiadjis & Kiousis [1987] are modified here in order to introduce rate sensitivity in the plastic region. Some of the basic concepts of the theory of viscoplasticity outlined by Naghdi & Murch [1963], Perzyna & Wojno [1966], and Eisenberg & Yen [1981] are used in this work in order to obtain the proposed viscoplastic constitutive model for finite strain deformation analysis.Uniaxial loading-reverse loading tests are conducted so as to check the validity of the proposed constitutive model as well as to determine its material parameters. The model is effectively used in simulating numerically the obtained experimental results at finite strains.     

网格湍流微结构的实验研究

本文试验研究了网格湍流从前期到后期整个连续衰变过程即湍能和Taylor微尺度随时间的变化规律,以及高阶速度相关系数的变化规律,试验结果是在一个低湍流度、低速风洞内,用TSI热线风速仪测得的,而拟均匀各向同性湍流是用在风洞试验段入口处加网格产生的,本文的试验结果与文献[1]提出的涡旋结构理论的计算结果做了比较,发现理论计算的和曲线与本文实测值非常吻合,本文的实测结果与Townsendt早年的试验以及Beanett七十年代末的试验也做了比较。结果表明,这些试验结果彼此也很一致,因而,所有这些试验结果与理论计算值都相互获得了验证。     

The motion of a sphere with weak nutation on a rough horizontal plane

ＴＨＥＭＯＴＩＯＮＯＦＡＳＰＨＥＲＥＷＩＴＨＷＥＡＫＮＵＴＡＴＩＯＮＯＮＡＲＯＵＧＨＨＯＲＩＺＯＮＴＡＬＰＬＡＮＥＹａｎｇＪｉ－ｙｉｎｇ（杨霁英）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＰｈｙｓｉｃｓ,ＳｈａｎｇｈａｉＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ...     

Three-dimensional stability theory of deformable bodies. Stability of construction elements

Conclusion In [8, 9] and in the present paper we analyzed the possibilities of using the approximate approach [15, 18] in the three-dimensional stability theory of deformable bodies as applied to effects of internal and surface instability and to stability of thinwalled structural elements. The analysis mentioned has been performed by comparing for standard problems the results obtained by the approximate approach [15, 18] with the results for the similar problems, obtained within the three-dimensional linearized stability theory of deformable bodies (for example [2–5, 7, 10, 19]), constructed with the accuracy usually adopted in mechanics. The following conclusions are drawn as a result of the analysis.Applied to effects of internal and surface instability, the approximate approach leads to result in disagreement with the corresponding results of the three-dimensional linearized stability theory of deformable bodies.As applied to the study of stability of thin-walled structural elements, the use of the approximate approach is justified if we restrict ourselves to a calculational accuracy of critical loads corresponding to that of the Kirchhoff-Love hypothesis.In connection with the discussion above, numerous publications carried out on the basis of the approximate approach require further study to clarify the validity limits of the results obtained.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 22, No. 2, pp. 3–17, February, 1986.     

Behavior of transversally isotropic cylindrical shells under dynamic application of radial pressure

We consider the problem on the buckling of a transversally isotropic long cylindrical shell under dynamic external pressure. For the cases of a sudden load [1] and a load rapidly increasing with time [2], we compare the results obtained from the two-dimensional Kirchhoff-Love and Timoshenko-Reissner theories.     

Nonstationary processes in starting strongly underexpanded jets

Results of the investigation of nonstationary efflux of argon by the electron-beam-sounding method are presented in [1]. Comparing the regularities obtained in that paper for the front motion of material during efflux from a nozzle with computations [2] for nonstationary expansion from a spherical source and the experimental results in [3] permitted clarification of the singularities of the influence of counter pressure and the temperature factor in jet expansion. The density distribution in nonstationary nitrogen and argon jets is obtained in this paper and study of the regularities of the front motion of the escaping gas is continued.Translated from Zhurnal Prikladnoi Mekhiniki i Tekhnicheskoi Fiziki, No. 1, pp. 34–40, January–February, 1978.     

有限弹塑性变形的三维组集式本构模型

本文将文[1]中提出的三维组集式弹塑性本构模型推广应用于有限变形分析,导出了全量型和增量型本构关系在初始构形上的拉格朗日(Total Lagrange)形式和瞬时构形上的拉格朗日(Updated Lagrange)形式。文中对晶体单轴拉伸中的宏观剪切带进行了分析。预测结果与实验吻合。从而说明这种本构模型能够模拟有限变形中的几何非线性效应和晶体材料塑性变形中的宏观力学行为。     

Strong viscous interaction on slender three-dimensional bodies

Hypersonic flow of a viscous gas past axisymmetric power-law bodies in the regime of strong interaction of the laminar boundary layer with the outer inviscid flow was studied in [1, 2]. In this paper the results obtained in [1, 2] are extended to the case of flow past a slender three-dimentional body.