具水平直裂纹的弹性半平面运动载荷问题

利用平面弹性复变方法和积分方程理论，讨论具水平直裂纹的弹性半平面运动载荷问题，最后，得出应力函数封闭形式的解。     

弹性长条的周期基本问题

Howland、唐立民、Isida 等对一个周期带内含有一个圆孔的弹性平面周期基本问题作了研究.把具有一个任意形状周期孔的平面弹性问题化为 Fredholm 积分方程.森口繁一在文献[4]§10中给出了在应力是周期的条件下函数的一般表达式,并分离出周期部分和非周期部分.路见可教授在文献[1]中把弹性平面或半平面中     

平面弹性理论的周期接触问题

对于平面弹性理论的经典接触问题,即弹性体(作为占有下半平面)上压着有限个压头的情况,和曾先后应用复变函数理论,得到了一些有效的解答,对于平面弹性理论的周期接触问题,即弹性体(作为占有下半平面)压着无限个按周期排列的压头,在所指弹性体为各向同性体的情况,路见可教授同样得到了     

基于厚板拉伸振动精确化方程求解动应力集中问题

过去,对拉伸平板考虑应力集中的工程设计多借鉴弹性力学平面问题分析求解结果,例如弹性力学Kirsch问题的解或弹性动力学平面问题的解．基于厚板拉伸振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究．研究结果表明:1) 两种模型得到的开孔附近的应力是不同的;2) 当入射波波数变大或者说入射波频率变高时,动应力集中系数最大值趋于单位1．含孔平板拉伸振动的动应力集中系数最大值达到3.30,以及基于弹性动力学平面问题模型得到的结果为2.77．对数值计算结果做了分析讨论, 可以看到,当孔径厚度比是a/h=0.10,基于平板拉伸振动精确化方程得到的动应力集中系数可以达到最大值,超出基于弹性动力学平面问题所得到结果的19%．分析方法和数值计算结果可望能在工程平板结构的动力学分析和强度设计中得到应用．     

带周期裂缝的弹性半平面问题

本文把具有任意形状和个数的周期裂缝的弹性半平面基本问题化为了某种特殊类型的奇异积分方程,证明了其解的存在和唯一。并对带周期共线直裂缝的弹性半平面问题,给出了封闭形式的解。     

点群6一维六方准晶椭圆孔口与半无限裂纹反平面弹性问题的解析解

导出了点群6-维六方准晶反平面弹性问题的控制方程.利用复变方法,给出了点群6-维六方准晶在周期平面内的反平面弹性问题的应力分量以及边界条件的复变表示,通过引入适当的保角变换,研究了点群6-维六方准晶中带有椭圆孔口与半无限裂纹的反平面弹性问题,得到了椭圆孔口问题应力场的解析解,给出了半无限裂纹问题在裂纹尖端处的应力强度因子的解析解.在极限情形下,椭圆孔口转化为Griffith裂纹,并得到该裂纹在裂尖处的应力强度因子的解析解.当点群6-维六方准晶体的对称性增加时,其椭圆孔口与半无限裂纹的反平面弹性问题的解退化为点群6mm-维六方准晶带有椭圆孔口与半无限裂纹的反平面弹性问题的解。     

一种用于平面弹性材料分析的有限元法

本文在有限元位移法的基础上,提出一种用于平面弹性材料机械性能分析的有限元法.利用这种方法及其微机程序,可以确定任一未知的平面弹性材料的机械性能,算出其全部弹性系数.     

双周期裂纹场的不同材料弹性平面焊接问题

本文讨论双周期胞腔中含若干个任意形状裂纹的不同材料的弹性平面焊接问题,根据路见可和方法,对这类弹性平面问题建立起了数学模型,将求解弹性平衡问题化归为寻求复应力函数的问题,并把路见可给出的复Airy函数用于推广方法,更进一步地将寻求复应力函数的问题归结为求解正则型的奇异积分方程,最后证明了其解存在且唯一。     

耦合热弹性平面问题的有限元法基本方程

本文在耦合热弹性问题变分原理的基础上,导出非定常温度场热弹性平面问题的有限元法基本方程.推导中,弹性平面划分为三节点三角形单元,时间过程划分为时间元,时间元中各变量(节点的位移和温度)随时间作线性变化.得出以各节点在每个瞬时(时间元的端点)的位移和温度为待定值的两组耦合的线性代数方程组,即基本方程.     

复合材料弹性平面的周期接触问题

对于平面弹性理论的经典接触问题,即弹性体(作为占有下半平面)上压着有限个压头的情况,曾应用复变函数理论,得到了一些有效的解答。对于平面弹性理论的周期接触问题,即弹性体上压着无限个按周期排列的压头,在所指弹性体为各向同性体的情况,路见可和蔡海涛同样应用复变函数理论,得到了一些有效解答。     

经济弹性函数的几何解释

弹性函数是研究当自变量有微弱变化时 ,函数的相对变化率 .本文构造一条初始弹性直线 ,弹性函数就是函数的切线斜率与初始弹性直线斜率之比 ;也是函数在弹性支点的微分与初始弹性直线在弹性支点的增量之比 .     

Polyconvex potentials,invertible deformations,and thermodynamically consistent formulation of the nonlinear elasticity equations

It is shown that the nonstationary finite-deformation thermoelasticity equations in Lagrangian and Eulerian coordinates can be written in a thermodynamically consistent Godunov canonical form satisfying the Friedrichs hyperbolicity conditions, provided that the elastic potential is a convex function of entropy and of the minors of the elastic deformation Jacobian matrix. In other words, the elastic potential is assumed to be polyconvex in the sense of Ball. It is well known that Ball’s approach to proving the existence and invertibility of stationary elastic deformations assumes that the elastic potential essentially depends on the second-order minors of the Jacobian matrix (i.e., on the cofactor matrix). However, elastic potentials constructed as approximations of rheological laws for actual materials generally do not satisfy this requirement. Instead, they may depend, for example, only on the first-order minors (i.e., the matrix elements) and on the Jacobian determinant. A method for constructing and regularizing polyconvex elastic potentials is proposed that does not require an explicit dependence on the cofactor matrix. It guarantees that the elastic deformations are quasiisometries and preserves the Lame constants of the elastic material.     

A generalized self-consistent method for composites with random elastic properties of inclusions

The generalized self-consistent method is extended to the problems of statistical mechanics of composites with random elastic properties of inclusions. This approach makes it possible to reduce the problem of predicting the effective elastic properties of composites with random structures to a sequence of simpler homogenized boundary-value problems for solitary inclusions with inhomogeneous elastic transition layers in a homogeneous effective elastic medium and with the corresponding boundary conditions. The elastic properties of a solitary inclusion for the gth homogenized problem are found from the solutions of the gth and (g+1)th homogenized problems. The elastic properties and sizes of the transition layers account for the random distribution, random sizes, and random elastic properties of inclusions in the composite. A test problem of predicting the effective elastic properties of a transversely isotropic layer composite with random elastic properties of some layers is solved by using the method proposed. The solution obtained coincides with the known exact solution [1].Perm State Technical University, Perm, Russia. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 6, pp. 785–796, November–December, 1999.     

一类弹性梁的能量衰减估计

研究一类弹性梁的耗散性.首先应用非线性算子半群理论证明了系统的适定性;进而运用能量方法结合乘子技巧得到弹性梁系统的能量衰减估计.     

Dispersion of elastic waves in a micropolar metamaterial plate with periodical arranged resonators

The wave propagation in a micropolar elastic metamaterial is investigated in this paper. The elastic metamaterial is composed of the micropolar elastic host material and the periodically arranged local resonators. Compared with the classical elastic metamaterial, the micropolar elastic metamaterial has more material parameters that can be elaborately designed to manipulate the elastic wave propagation. By introducing additional displacement fields, a multi-displacement continuum model of the micropolar elastic metamaterial is presented to characterize the resonance behavior of the resonators and the microstructure effects of the unit cell. According to this continuum model, two independent wave systems exist: one is a longitudinal system and the other is a shear and rotation coupled transversal system. The dispersive curves and band gaps of the longitudinal and transversal systems are numerically discussed and the influences of the resonators are mainly considered.     

不同材料的两个各向同性弹性长条的焊接问题

利用复变方法和积分方程理论 ,讨论两个不同材料的各向同性弱性长条的焊接问题 ,在理论上 ,给出了弱性体应力分布封闭形式的解 .     

Small amplitude, free longitudinal vibrations of a load on a finitely deformed stress-softening spring with limiting extensibility

A constitutive theory for a general class of incompressible, isotropic stress-softening, limited elastic rubberlike materials is introduced. The model is applied to study the small amplitude, free longitudinal vibrational frequency of a load about a suspended static equilibrium stretch of a finitely deformed, stress-softening spring with limiting extensibility. A number of physical results, including bounds on the frequency, are reported. It is proved, for example, that the normalized vibrational frequency for the ideally elastic neo-Hookean oscillator is a lower bound for the normalized frequency of every incompressible, isotropic stress-softening, limited elastic oscillator within the general class. All results are illustrated for the special limited elastic Gent and the purely elastic Demiray biomaterial models, both with stress-softening characterized by a Zú?iga–Beatty front factor damage function. The results for both stress-softening models are compared with experimental data for several gum rubbers and thoracic aortic tissue provided by others; and, overall, it is found that the stress-softening, limited elastic Gent model best characterizes the data.     

The existence of riemann invariants in the one-dimensional equations of the non-linear theory of elasticity

The conditions for the existence of Riemann invariants of a one-dimensional system of equations of the non-linear theory of elasticity are investigated. Haantjes' diagonalization criterion is used to determine the form of the elastic potential for which the system has six Riemann invariants or three Riemann invariants (for waves which propagate in one direction). In particular, it is shown that the Haantjes criterion is satisfied and there are three Riemann invariants in the case of the elastic potential for slightly-non-linear weakly-anisotropic elastic media [1–3]. A procedure for computing Riemann invariants is described. The Riemann invariants are computed approximately for a form of elastic potential which satisfies the Haantjes criterion.     

Discussion of Different Model Approaches for the Flow Behavior of Ice

Ice of Antarctic ice shelves is assumed to behave on long-term as an incompressible viscous fluid, which is dominated on short time scales by the elastic response. Hence, a viscoelastic material model is required. The thermodynamic pressure is treated differently in elastic and viscous models. For small deformations, the elastic isometric stress for ν → 0.5 gives similar results to those solving for pressure in an incompressible laminar flow model. A viscous model, in which the thermodynamic pressure is approximated by an elastic isometric stress, can be easily extended to viscoelasticity. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

一类变形Euler棒P-稳定性的研究

借助于特征根法研究Euler弹性棒变形的P稳定性.将广泛存在于应用技术中的一类弹性单元抽象为Euler弹性棒,建立相应变形的物理和数学模型-常微分方程的边值问题,将其嵌入偏微分方程,得到数学模型解的P-稳定性.