Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening

Energy-coupled stress and strain measures are defined in Euler coordinates. They are used to analyze the relationship between the first invariants of the stress and strain tensors for linearity and to determine strains at which the plastic component of the first strain invariant can be neglected. It is established that this relationship remains linear within an engineering plastic-strain tolerance of 0.2% irrespective of the value of strain intensity, which depends on the type of material and its stress state __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 60–72, March 2007.     

非对称的非局部塑性理论

从非局部连续场论出发，假定形变与局部转动均属微小，当存在体力矩出现非对称应力场时，设对称应力的能量函数和非对称应力的能量函数可以独立计算。基于热力学原理和屈服面的概念，建立了一种新的非对称－非局部弹塑性力学理论。     

Reynolds数对大攻角细长旋成体绕流滚转角效应影响的数值研究

使用低耗散的Roe格式,数值模拟了Reynolds数(Re)对大攻角细长旋成体绕流滚转角效应的影响.模型头部加了几何小扰动块以引发流场的不对称.在较大的Re数(Re=10 5)下,本文的计算结果与实验是相符的,此时细长体的滚转会导致双稳态、双周期现象,即侧向力随滚转角呈现类似方波形式的双周期变化,方波中侧向力基本保持不变的状态对应于流场的正则态,且两个正则态的侧向力方向相反,方波中侧向力基本保持不变的状态对应于流场的正则态,且两个正则态的侧向力方向相反;而在较小的Re数(Re=4 000)下,如果扰动足够大,细长体的滚转将导致不同的双稳态现象,此时两个正则态的侧向力方向相同,而在较小扰动下双稳态现象不再出现;Re数更小时(Re=1 000),即使在较大的扰动下,双稳态现象也不再出现,侧向力随滚动角仍是连续变化的.本文的计算结果表明,Re数越小,流场对头部扰动的感受性越弱.     

轴对称弹性体扭转问题的无网格自然邻接点Petrov-Galerkin法

本文将无网格自然邻接点Petrov-Galerkin 法应用于轴对称弹性体扭转问题的求解．无网格自然邻接点Petrov-Galerkin 法采用自然邻接点插值构造试函数，并且采用三角形线性单元的形函数作为加权残值法的加权函数．自然邻接点插值构造的试函数满足Kronecker delta 函数性质，因此本质边界条件的施加十分方便．由于几何形状和边界条件的轴对称特点，原来的空间问题简化为二维问题求解，因此计算时只需要横截面上离散节点的信息．数值算例结果表明，所提出的方法对求解轴对称弹性体扭转问题是行之有效的．     

轴对称物体内三维残余应力场的确定

三维残余应力场的测量理论是国内外未能解决的问题.本文建立了新的轴对称空间力学模型,介绍了对45钢140×200圆柱体进行内剥层测量的实验.在分析中引入了罐载和非罐载应力的概念,为正确处理变动的边界条件给出了思路、使得空间力学模型真实地反映了轴对称体内残余应力的实质.在求解中提出了变应力函数及其解法,使得轴对称三维残余应力场的测量理论得到了真正解决.     

Supersonic transverse rarefied gas flow past a strip

The supersonic flow of a monatomic gas consisting of hard spherical particles past a flat strip normal to the flow is investigated using the direct simulation Monte-Carlo (DSMC) method. The calculations are performed over the Knudsen and Mach number ranges 0.015–5 and 1.8–15, respectively. The structure of the compressed layer and the aerodynamic characteristics are systematically studied for the Mach number 5 and various Knudsen numbers. The dependences of the compressed-layer thickness in molecular free paths are found. The nonequilibrium processes in the neighborhood of the strip are described on the basis of the data on the temperature anisotropy with respect to three coordinates.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, 2005, pp. 159–167. Original Russian Text Copyright © 2005 by Maltsev and Rebrov.     

Variational methods of solving dynamic problems for fluid-containing bodies

A variational approach to solving linear and nonlinear problems for a body with cavities partially filled with a perfect incompressible fluid is enunciated. The approach applies a nonclassical variational principle to describe the spatial motion of a finite fluid with a free surface and the classical variational principle, which is widely used in rigid body dynamics. These principles are used to formulate variational problems that are the basis of direct methods of solving nonlinear and linear dynamic problems for body-fluid systems. The approach allows us to derive an infinite system of nonlinear ordinary differential equations describing the joint motion of the rigid body and fluid and to develop an algorithm for determining the hydrodynamic coefficients. Linearized differential equations of motion of the mechanical system are presented and approximate methods are given to solve linear boundary-value problems and to determine the hydrodynamic coefficients.Translated from Prikladnaya Mekhanika, Vol. 40, No. 10, pp. 37–77, October 2004.The study was partially sponsored by the German Research Fund (der Deutsche Forschungsgemeinschaft), Grant 436 UKR113/33/0-3.     

On the Formation of Discontinuities of Wave Fronts in a Saturated Granular Body

The paper deals with propagation of plane wave fronts in a solid with a non-linear relation between stress and deformation. The objective is to calculate the distance that a wave front covers before it loses continuity. The formulae derived for a general quasi-linear system of two equations are applied to the propagation of plane compression waves in dry and partially saturated granular bodies. In the case of a saturated body with gas bubbles, the influence of gas and capillary pressure on the stiffness of the body is taken into account. Numerical calculations relevant to soil mechanics are presented. For the numerical calculations a constitutive equation of the hypoplasticity theory for granular materials has been used. Received November 1, 1997     

Flow past an axisymmetric body embedded in a saturated porous mediumÉcoulement derrière un corps à symétrie axiale plongé dans un milieu poreux saturé

The problem of viscous fluid past an axisymmetric body embedded in a fluid saturated porous medium is studied using the Brinkman's extension. A general formula for the drag on the body is derived in the form of a limit of an expression involving the stream function characterizing the flow. The flow past an axisymmetric approximate sphere is also considered. The stream function in this case is obtained in terms of Bessel functions and Gegenbauer's functions. The drag acting on the body is evaluated by using the formula derived. Its variation is studied with respect to geometric and permeability parameters. The special cases of flow past a sphere and a spheroid are obtained from the present analysis. To cite this article: D. Srinivasa Charya, J.V. Ramana Murthy, C. R. Mecanique 330 (2002) 417–423.     

Inequalities relating to Lp-version of Petty＇s conjectured projection inequality

Petty＇s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to Lp-version of the Petty＇s conjectured projection inequality is developed by using the notions of the Lp-mixed volume and the Lp-dual mixed volume, the relation of the Lp-projection body and the geometric body Г-pK, the Bourgain-Milman inequality and the Lp-Bnsemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Г-pK, the reverses of Lp-version of the Petty＇s conjectured projection inequality and the Lp-Petty projection inequality are given, respectively.