功能梯度空心及实心圆柱体旋转时的弹性及粘弹性解

逐步分析了旋转的功能梯度空心及实心长圆柱体问题的解.假设圆柱体的弹性模量和材料密度沿径向呈指数变化,Poisson比为常数.由平衡方程、相容方程、弹性变形理论及应力-应变关系,导出了统一的控制方程.根据超几何函数,求解该二阶微分控制方程,得到旋转功能梯度圆柱体的弹性变形.检验并讨论了圆柱体中的应力与非均质参数、几何、边界条件之间的相互关系.将旋转功能梯度空心及实心圆柱体的分析结果,与旋转均质各向同性圆柱体的结果进行了对比分析.同时,提出了旋转粘弹性圆柱体的粘弹性解,并验证了空心及实心圆柱体中应力与时间参数间的依赖关系.     

功能梯度厚壁中空圆柱体弹性动力学平面应变响应的解析解

研究了边界表面受均布动压力作用的功能梯度(FGM)厚壁中空圆柱体,给出了其平面应变响应下的弹性动力学解．假设材料性能(除Poisson比外)随厚度按幂律函数变化．为了得到一个精确解,将动力径向位移分为准静力部分和动力部分,导出了每个部分的一个解析解．先由Euler方程得到准静力学部分的解,再由分离变量法和正交展开法得到动力学部分的解．在不同动荷载作用下,对不同的FGM中空圆柱体,画出径向位移和应力图,并对本方法的优点进行了讨论．该解析解适用于中空圆柱体各种组合的FGM,厚度可以是任意的,初始条件也可以是任意的,壁面上均匀分布着任意形式的动压力．     

无限非均质横观各向同性黏弹性介质中具有圆柱孔洞时的振动

在无限介质中,研究了横截面为圆的柱形孔洞表面上瞬时径向力或扭转引起的扰动,讨论了高阶黏弹性和横观各向同性弹性参数的非均匀性对扰动产生的影响．根据高阶黏弹性Voigt模型,将非零应力分量简化为径向位移分量项表示,这对横观各向同性和高阶黏弹性固体介质是合宜的．导出了含有弹性和黏弹性参数以幂律变化时的应力方程．在瞬时力和扭转边界条件下,求解该方程,求得径向位移分量以及和它相关的应力分量,用修正的Bessel函数项来表示．对瞬时径向力作用问题进行了数值分析,并给出了不同阶的黏弹性和非均质性时的位移和应力变化图形．扭转作用时扰动的数值解可以用类似的方法研究,这里不再深入讨论．     

Elastic Analysis of Anisotropic Functionally Graded Rotating Disks With Non-Uniform Thicknesses北大核心CSCD

研究了任意梯度变化的变厚度各向异性转动圆盘的弹性问题.假设圆盘绕刚性轴匀速转动,其材料性能和厚度沿径向任意梯度变化.考虑圆盘在中心转轴处受位移约束,外侧自由,根据各向异性转动圆盘的平衡微分方程,得到关于径向应力的Fredholm积分方程,继而通过对Fredholm积分方程进行数值求解,得到结构的位移场和应力场.对具体梯度变化情况仅需代入相应梯度变化进行求解即可.数值算例部分,通过假设厚度、弹性模量等参数为特殊的幂函数形式,将由Fredholm积分方程求出的数值解与对应的精确解进行对比,以及针对常见的Voigt模型,将由该方法算得的数值解和ANSYS有限元计算结果进行对比,验证了该方法的准确性和精度.其次,针对Voigt模型,重点分析了厚度变化、材料性能梯度参数、各向异性度等对应力场和位移场的影响.提出了针对材料性能和厚度沿径向呈任意梯度变化的圆盘结构弹性分析方法,将为优化功能梯度圆盘的结构和材料参数、有效调整构件应力分布、提高结构安全性,提供强有力的工具;算例分析结果对功能梯度圆盘在复杂条件下的结构安全设计有重要的理论指导意义.     

无限圆柱体旋转运动时的热应力

研究旋转对确定边界条件下无限圆柱体的影响.当热荷载沿径向作用时,给出了旋转圆柱体中热应力、位移和温度的分析过程.当无限弹性圆柱体部分弯曲界面有常温作用,而其余界面维持零温度时,讨论其热动应力的分布.圆柱体表面绝缘材料熔化时出现这种情况.得到了应力分量、位移分量和温度的解和数值结果.提出的半解析法所得到的结果,与早期采用方法所得到的结果比较,发现两者显示出很好的一致性.     

双筒流变仪中粘弹性流体的解析解及运动特性分析

求得二阶流体和Maxwell流体在环管内不定常旋转运动问题的解析解.据此可以分析环管内旋转速度和切应力分布与变化特征.流体的物性常数、管道环隙大小等参数在解析公式中有明确反映,便于分析与讨论.本解可以用来分析类似的工程流动问题,尤其更具有针对性的是分析双筒流变仪中流动特征与应力状态,确定材料的粘弹性参数.通过计算,发现当外筒作简谐振动时,Maxwell流的速度和切应力变化曲线上有突变结,突变结上振幅和相位都发生突变.当外筒匀速旋转时,Maxwell流体的速度和切应力变化曲线分别呈斜方波和锯齿波形状.振动周期与材料常数H_a二次曲线相关.     

均布载荷作用下各向异性固支梁的解析解

针对均布载荷作用下的各向异性梁在两端固支条件下的平面应力问题,给出了一个求解应力和位移解析解的方法．该方法构造了一个含待定系数的应力函数,通过Airy应力函数解法,给出了含待定系数的应力和位移通式．对固支端边界条件采用两种处理办法．利用应力和位移边界条件,确定应力函数中的待定系数,得到了应力和位移的解析表达式．结果表明,该解析解与有限元数值结果相比,两者较为吻合．该解析解是对弹性理论中相关经典例题的补充．     

二维弹性平面问题中任意边界条件下应力分布的封闭解

应用辛方法研究了正交各向异性二维平面（x,z）弹性问题,在任意边界和不考虑梁假设条件下的解析应力分布解．辛方法通过将位移和应力作为对偶量推导得到一组辛的偏微分方程组,并且应用变量分离法对方程组进行了求解．同动力学中的问题比较,将弹性问题中的x轴模拟成时间轴,这样z轴成为唯一一个独立的坐标轴．问题中的Hamilton矩阵的指数展开具有辛的特征．在齐次问题求解中,通过边界条件和边界上的积分求得级数中的未知数．齐次解中包括减阶的零特征值的特征向量（零本征向量）和完好的非零本征值的特征向量（非零本征向量）．零本征值的Jordan链给出了经典的Saint Venant解,反映了平均的整体行为像刚体位移、刚体旋转和弯曲等．另外,非零本征向量反映的是指数衰减的局部解,它们通常在Saint Venant原理下被忽略．文中给出了完整的算例,并且和已有结果进行了对比．     

任意厚度具有自由边叠层板的精确解析解

自由边问题一直是三维弹性力学中的难题,通常很难满足自由边上一个正应力和两个剪应力都等于0．基于三维弹性力学基本方程和状态空间方法,引入自由边界位移函数并考虑全部弹性常数,建立了正交异性具有自由边单层和叠层板的状态方程．对状态方程中的变量以级数形式展开,通过边界条件的满足精确求解任意厚度具有自由边叠层板的位移和应力,此解满足层间应力和位移的连续条件．算例计算表明,采用引入的位移函数形式,简化了计算过程并且采用较少的级数项可以获得收敛解．与有限元方法计算结果进行了对比,可以得到较高精度的数值结果．其解可以作为其它数值方法和半解析方法的参考解．     

含裂纹的圆柱体的弯曲

含裂纹的圆柱体弯曲的研究有十分重要的意义。文献[1]～[4]研究过含径向裂纹或裂纹系的情形,[5]研究过有同心圆弧裂纹的圆柱体的弯曲。本文继续[6]对内部出现在任意位置的直线裂纹的圆柱体在力与裂纹垂直时的弯曲问题,用弹性理论复变函数方法进行了讨论;得到了位移、应力和应力强度因子用级数表示的表达式;对Ah小的这种弯曲问题的应力强度因子给出了好的近似式,分析了它们随裂纹中心的变化规律。最后对裂纹的一个尖端在原点的径向裂纹圆柱体的扭转率和弯曲中心进行了计算,其结果与[1]几乎完全相同。     

Dynamic stability of axisymmetrically heated glass-reinforced plastic cylindrical shells bonded to elastic cylinders

The dynamic stability of glass-reinforced plastic shells subjected to the action of a longitudinal pulsating force and an external, uniformly distributed load is examined. The shells are orthotropic, and their elastic properties are temperature-dependent and vary over the thickness of the wall. It is assumed that the elastic cylinder forms a Winkler foundation. Three boundary conditions are investigated.Moscow Institute of Chemical-Machine Building. Translated from Mekhanika Polimerov, No. 2, pp. 331–337, March–April, 1972.     

Propagation of unsteady waves in a hollow magnetoelastic cylinder in contact with liquid media

A numerical-analytic solution is constructed for the problem of magnetoelasticity for a hollow cylinder immersed in a liquid and loaded from inside by an impulse-type axisymmetric mechanical pressure. Nonconducting and compressible internal and external media have different densities and elastic moduli, with their motion described by wave equations. The hollow cylinder is assumed to be an ideal conductor, and its motion is described by a linearized system of equations of magnetoelasticity; on internal and external boundaries, the conditions of conjugation hold. The problem is solved by the method of integral Laplace transforms in the time domain, and the inverse transforms are found by numerical inversion. The solutions obtained for the bounded problem are compared with solutions for a simplified unbounded problem.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 83–87, 1987.     

Dynamic electromechanical behavior of a triple-layer piezoelectric composite cylinder with imperfect interfaces

The dynamic electromechanical behavior of a triple-layer piezoelectric composite cylinder with imperfect interfaces is investigated. The composite cylinder is constructed by two elastic layers and an embedded piezoelectric layer. A linear spring model is adopted to describe the weakness of imperfect interface. The exact analysis is performed by the state space method and normal mode expansion method. The determining procedure for the eigenfunction and the proof of the orthogonal property of the eigenfunction is presented for an imperfectly bonded triple-layer piezoelectric composite cylinder. The obtained solution is valid for analyzing the dynamic electromechanical behavior of composite cylinder with arbitrary thickness for both elastic and piezoelectric layers. Numerical results show that the weakness of imperfect interface has significant effect on the transient electromechanical responses of piezoelectric composite cylinder.     

Stability of orthotropic cylindrical shells under variable pressure

A method of determining the critical stresses is developed for elastic orthotropic cylindrical shells subjected to nonuniform pressure. It is assumed that the external pressure varies over the cross section and is constant along the length of the cylinder. A shell stability analysis is given for the case of a weakly varying load.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Mekhanika Polimerov, No. 5, pp. 897–902, September–October, 1970.     

Scattering of impulsive elastic waves b a fluid cylinder

We consider the scattering of impulsive sv waves by a fluid circular cylinder. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with some acoustic fluid. The line source, generating the incident pulse is situated outside the cylinder parallel to its axis. We investigate the problem by the method of dual integral transformation as developed by Friedlander. The resulting integrals are evaluated approximately to obtain the short time estimate of the motion near the wave-front in the illuminated region of the elastic medium. We also interpret the approximate solution in terms of geometrical optics.     

Optimization of the stressed state by a distribution of elastic parameters in elastic bodies

For designing an isotropic inhomogeneous body having a variable elastic modulus and a prescribed shape under the influence of an external force load we give a formulation and solution of the problem of determining the design that is optimal with respect to stress. The problem of optimal design reduces to a certain problem in the theory of elasticity for a non-linearelastic material. As an example we consider the problem of optimal design of an inhomogeneous cylinder. Four figures. Bibliography: 9 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 78–82.     

Diffraction of impulsive elastic waves by a fluid cylinder

We consider the diffraction of impulsive SV waves by a fluid circular cylinder. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with some acoustic fluid. The line source, generating the incident pulse, is situated outside the cylinder parallel to its axis. We investigate the problem by the method of dual integral transformation as developed by Friedlander. The resulting integrals are evaluated approximately to obtain the short-time estimate of the motion near the wave front in the shadow zone of the elastic medium. We also interpret the approximate solution in terms of Keller’s geometrical theory of diffraction.     

The coupling system of Navier–Stokes equations and elastic Navier–Lame equations in a blood vessel

In this paper, the blood flow problem is considered in a blood vessel, and a coupling system of Navier–Stokes equations and linear elastic equations, Navier–Lame equations, in a cylinder with cylindrical elastic shell is given as the governing equations of the problem. We provide two finite element models to simulating the three-dimensional Navier–Stokes equations in the cylinder while the asymptotic expansion method is used to solving the linearly elastic shell equations. Specifically, in order to discrete the Navier–Stokes equations, the dimensional splitting strategy is constructed under the cylinder coordinate system. The spectral method is adopted along the rotation direction while the finite element method is used along the other directions. By using the above strategy, we get a series of two-dimensional-three-components (2D-3C) fluid problems. By introduce the S-coordinate system in E³ and employ the thickness of blood vessel wall as the expanding parameter, the asymptotic expansion method can be established to approximate the solution of the 3D elastic problem. The interface contact conditions can be treated exactly based on the knowledge of tensor analysis. Finally, numerical test shows that our method is reasonable.     

The steady motion of an elastic cylinder compressed by a fixed shell

The steady mixed problem of the motion of a transversely isotropic elastic circular cylinder, compressed by a finite elastic shell, is solved by the method of piecewise-homogeneous solutions [1]. One of the relations of generalized orthogonality obtained for homogeneous solutions is used. Two special cases are considered: (1) a semi-infinite shell is placed on a movable cylinder with a specified negative allowance the edge of the shell is stress-free, and there is no preloading, and (2) a concentrated encircling load acts on the shell. The solution of the problem of a semi-infinite shell and the system of piecewise-homogeneous solutions are constructed in quadratures by the Wiener-Hopf method. (A similar problem was investigated in [2] in a static formulation. Steady mixed contact problems were investigated previously in [3–10]).     

Torsional wave propagation in a pre-stressed circular cylinder embedded in a pre-stressed elastic medium

Within the framework of the piecewise homogeneous body model with utilization of the three-dimensional linearized theory of elastic waves in initially stressed bodies, the mathematical modeling of the torsional wave propagation in the initially stressed infinite body containing an initially stressed circular solid cylinder (case 1) and circular hollow cylinder (case 2) are proposed. In these cases, it has been assumed that in the constituents of the considered systems there exist only the normal homogeneous tensional or compressional initial stress acting along the cylinder, i.e. in the direction of wave propagation. In the case where the mentioned initial stresses are not present, the proposed mathematical modeling coincides with that proposed and investigated by other authors within the classical linear theory of elastic waves. The mechanical properties of the cylinder and surrounding infinite medium have been described by the Murnaghan potential. The numerical results related to the torsional wave dispersion and the influence of the mentioned initial stresses on this dispersion are presented and discussed.