Stability of Plates Made of Fibrous Composite with Damageable Components

The bifurcation stability problem for rectangular plates made of fibrous composite with damageable matrix is formulated and solved__________Translated from Prikladnaya Mekhanika,Vol. 41, No. 5, pp. 83–90, May 2005.     

Stability of Shells of Revolution Made of Fibrous Composite with Damageable Matrix

The bifurcation-stability problem for shells of revolution made of fibrous composite with damageable matrix is formulated and solved. Increase in the damage of the matrix under loading is taken into account __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 10, pp. 75–83, October 2005.     

Stability of Cylindrical Shells Made of Fibrous Composite with Damageable Matrix

The bifurcation stability problem for cylindrical shells made of fibrous composite with damageable matrix is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 105–112, June 2005.     

有环壳过渡段的锥—柱组合壳的应力和稳定性

用解析方法计算了受静水外压载荷作用的有环壳过渡段的锥—柱组合壳中的应力值，并用瑞利法计算了其失稳临界载荷。计算结果说明，利用环壳过渡值锥—柱壳形成光滑连接，可使连接部位的局部应力值显著降低，并使失稳临界载荷有所提高     

Stability of plates made of a damageable physically nonlinear material

The bifurcation instability problem for rectangular plates made of physically nonlinear materials progressively damaged with increasing load is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 79–88, September 2006.     

钻孔法和光栅应变花测试复合材料的残余应力

残余应力对材料、结构的疲劳强度和使用寿命等性能的影响早已为人们所熟知,由于它的大小、方向和分布随制造加工或处理方法不同而有很大的随机性,国内外对它的研究很重视。对于各向异性的复合材料,随着加上生产制造过程及工艺参数的不同,其中的残余应力的大小、方向等就更加复杂。从国内外对残余应力的研究中,可以看出大多数都着重于实验研究。本文应用钻孔法和云纹干涉技术的成果,针对残余应力测试中的特点,尤其是在利用钻孔法和云纹干涉技术测试残余应力时存在的问题,在目前绝大多数云纹干涉技术所使用的正交光栅的基础上,提出并研制出一种三个方向的光栅,即在原来 0°、90°两个方向光栅上,再加上一个 45°方向的光栅,在进行云纹干涉测试时,一次加载时就可以同时测试出三个独立的位移场:u场、v场和s场,利用这三个位移场就可以得到相应的三个应变:ε0、ε90和ε45,进而可以计算得到相应的应力。     

Stability of shells of revolution made of a damageable nonlinear elastic material

The problem of bifurcation instability of shells of revolution made of a nonlinear elastic material progressively damaged under loading is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 35–45, May 2007.     

Stability of plates made of a particulate composite with nonlinear elastic matrix and damaged inclusions

The bifurcation instability problem for rectangular plates made of particulate composites with nonlinear elastic matrix and damaged inclusions is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 79–89, July 2007.     

Stability of a rectangular plate under biaxial tension

The stability problem of a rectangular plate undergoing uniform biaxial in-plane tensile strain is solved using the three-dimensional equations of nonlinear elasticity. The surfaces of the plate are stress-free, and special boundary conditions that allow one to separate variables in the linearized equilibrium equations are specified on the lateral surfaces. For three particular models of incompressible materials, the critical curves are constructed and the instability region is determined in the plane of the loading parameters (the multiplicities of elongations of the plate material in the unperturbed equilibrium state). The numerical results show that for thin plates loaded by tensile stresses, the size and shape of the instability region depend only slightly on the relation among the length, width, and thickness of the plate. Based on the results obtained, a simple approximate stability criterion is proposed for an elastic plate under tensile loads. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 94–103, July–August, 2007.     

Stability of cylindrical shells made of a particulate composite with nonlinear elastic inclusions and damageable matrix

The bifurcation instability problem for cylindrical shells made of particulate composites with nonlinear elastic inclusions and damageable matrix is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 68–79, October 2007.     

考虑几何与材料及静风荷载的非线性因素的大跨径桥梁静风稳定分析法

针对现有的桥梁静风稳定分析方法中存在的问题，提出了增量与内外两重迭代相结合的新方法，并且考虑了结构几何、材料和静风荷载非线性。在上述方法的基础上，编制了桥梁非线性空气静力稳定分析程序BNAP，并进行了相应的算例分析，所得结果表明该方法具有计算稳定和速度快的优点。最后，以一座主跨1000米的斜拉桥为例，分析了结构几何非线性、材料非线性和静风荷载非线性对大跨径桥梁空气静力稳定性的影响。     

Stability and initial postbuckling behavior of anisotropic cylindrical shells under external pressure

A solution is obtained to describe the stability and initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry. The solution is based on the Donnell-Mushtari-Vlasov nonlinear theory of anisotropic shells and Koiter’s theory of buckling and postbuckling behavior. Calculated results are presented for boron plastic shells with reinforcement of different types under external pressure. It is shown that the conventional model of a composite as an orthotropic material is erroneous for many types of reinforcement __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 86–103, March 2007.     

Stability of shells of revolution made of a particulate composite with nonlinear elastic inclusions and damageable matrix

The bifurcation instability problem for shells of revolution made of particulate composites with nonlinear elastic inclusions and damageable matrix is formulated and solved __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 11, pp. 55–65, November 2007.     

Dynamics of a prestressed incompressible layered half-space under moving load

The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The elastic potential is given in general form and is only specified for numerical purposes. The dependence of the critical velocity of the load and the stress-strain state on the prestresses is analyzed for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations are carried out for a half-space with Bartenev-Khazanovich potential __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 36–54, March 2008.     

粘性金属中的正激波稳定性问题

G.H.Miller等把高压金属中的粘性激波作为强间断面处理,解析推论出:在大粘性系数条件下小扰动激波是不稳定的,物质粘性是导致失稳的因素。本文中针对平面正激波,认为高压金属中的粘性激波的物理量是连续变化的,利用线性稳定性理论,用数值解推论出:在有粘性条件下小扰动激波都是稳定的,物质粘性是致稳的因素。指出G.H.Miller等获得错误结论的原因在于:从无粘流动解推出的小扰动边界条件导致粘性激波小扰动增长。给出实验确定的小扰动速度梯度的边界条件,这样既可以把粘性正激波作为强间断面处理,也能够保证粘性正激波的稳定性。     

Kink Surfaces in a Directionally Reinforced neo-Hookean Material under Plane Deformation: II. Kink Band Stability and Maximally Dissipative Band Broadening

Stationary kinks (elastostatic shocks) are examined in the context of a base neo-Hookean response augmented with unidirectional reinforcing that is characterized by a single additional constitutive parameter for the additional fiber reinforcing stiffness. Previous work has shown that such a transversely isotropic material can support stationary kinks in plane deformation if the reinforcing is sufficiently great. If the deformation on one side of the kink involves a load axis aligned with the fiber axis, then the more general plane deformation on the other side of the kink is characterized in terms of a one-parameter family of (kink orientation, kink strength)-pairs. Here, the ellipticity status of the two correlated deformation states is shown to span all four possible ellipticity/nonellipticity permutations. If both deformation states are elliptic, then a suitable intermediate deformation is shown to be nonelliptic. Maximally dissipative quasi-static kink motion is examined and interpreted in terms of kink band broadening in on-axis loading. Such maximally dissipative kinks nucleate only in compression as weak kinks, with subsequent motion converting nonelliptic deformation to elliptic deformation. The associated fiber rotation involves three periods: an initial period of slow rotation, a secondary period of rapid rotation, and a final period of essentially constant orienation.     

Stability of the Interface of a Liquid-Suspension System under High-Frequency Nonlinearly Polarized Vibration

The stability of the state of a two-layer system consisting of a homogeneous liquid and a solid particle suspension in the same liquid with a plane interface between them is investigated. The system performs both horizontal and vertical high-frequency vibration with an arbitrary phase shift. It is shown that a mean flow develops under the simultaneous action of both horizontal and vertical vibration; quantitative flow stability characteristics are determined numerically using the differential sweep method. It is shown that a traveling wave relief exists on the liquid-suspension interface. Transverse oscillations in phase with longitudinal oscillations destabilize the entire system. The presence of an oscillation phase shift can lead to an increase in the stability limit; the direction of motion of the wave relief can differ depending on the value of the phase shift. Instability of the system in the presence of strictly vertical vibration is observed, the crisis being associated with longwave monotonic perturbations.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 3–13.Original Russian Text Copyright © 2005 by Lobov, Lyubimov, and Lyubimova.     

Theory of Short-Term Microdamageability for a Homogeneous Material under Physically Nonlinear Deformation

The structural theory of short-term damageability is generalized to the case of physically nonlinear deformation of an undamaged material. The stochastic elasticity equations for a porous medium whose skeleton deforms nonlinearly are used. The failure criterion for a microvolume of the material is assumed to be in the Huber–Mises form. The microdamage balance equation for a physically nonlinear material is derived. This equation and the macrostress–macrostrain relation for a porous physically nonlinear material constitute a closed-form system describing the coupled processes of physically nonlinear deformation and microdamage. An algorithm is constructed for computing microdamage–macrostrain relationships and plotting deformation curves. Such curves are plotted for the case of uniaxial tension     

热超弹性薄板非对称拉伸的分岔和稳定性

本文应用超弹性材料的有限变形理论分析了在面内等双向拉伸死载荷作用下不可压热超弹性方形薄板发生非对称变形的分岔及其稳定性问题.给出了方板变形的分岔曲线和临界载荷,发现对受面内等双向拉伸载荷作用的均匀方板,当拉伸载荷值较小时,方板双向等伸长变形,发生对称的拉伸变形;但当此载荷值大于某一临界值时,从方板的对称拉伸变形中分岔出非对称的变形,方板在两个方向的变形不再相等.通过变形发生分岔前后的能量比较发现,分岔后的对称变形是不稳定的,而非对称变形是稳定的.同时,给出了板中的应力分布曲线,并由不同温度下变形的分岔曲线和应力分布曲线讨论了温度对方板变形和板中的应力分布的影响.     

Stability of elastic and viscoelastic systems under a random perturbations of their parameters

Summary The present paper is concerned with the investigation of the almost sure stability of elastic and viscoelastic systems, when their parameters assume a random wide-band stationary process. The parameters are parametric loads, characteristics of external damping and material viscosity. With the help of Liapunov's direct method, the sufficient condition of the almost sure asymptotic stability for distributed parameter systems with respect to perturbations of initial conditions of an arbitrary form is obtained. It is shown that, in some cases, this condition coincides with a similar condition derived from the assumption that the form of sure and required perturbations coincides with the first eigenfunction of system oscillations. However, an example is given for the stability of a viscoelastic rod, when the perturbations of initial conditions are more dangerous, if their form differs from the first eigenfunction.This research was sponsored by the Russian Foundation of Fundamental Research of the Russian Academy of Sciences under Grant 94-01-01522.