Simplification of Frequency Equation of Multilayered Cylinders and Some Recursion Formulae of Bessel Functions

本文从理论上研究了相同材料的多层厚壁圆筒径向振动的频率方程, 证明若干层相互接触的层筒的整体频率方程, 可以用单个厚壁圆筒的频率方程替代, 从而大大简化了求解过程。并从该实际问题出发,推导出了一类贝塞尔函数的递推公式。     

Sachs法的应用及推广

本文提出测量平面应力状态厚壁圆筒残余应力时Sachs公式的简化,特别提出了测量和计算具有轴向残余应力有限长厚壁圆筒残余应力的方法.这些结果可用于研究火炮自紧身管内的残余应力.     

具有初始层间压力的层合圆筒的热冲击研究

采用一种解析方法求解具有初始层间压力的双层层合圆筒内的动态热应力的瞬态响应·　首先,将由自紧装配双层层合圆筒引起的初始层间压力考虑作为热弹性动力学方程的初始条件·　其次,利用一个简便的数学变换方法求解具有初始应力场的单层圆筒的热弹性动力学解,然后利用层合圆筒的边界条件和连接条件,得到具有初始层间压力的双层层合圆筒的热冲击解·     

圆筒受余弦分布压力之解及其k→0的极限

本文得到一个新的应力函数。用此解答了圆筒受余弦分布压力的问题,并为解决圆筒在轴向受任意分布荷载作用的空间轴对称问题打下了基础。根据求出的解答,取压力沿轴向不变化时的极限,就导出了厚壁圆筒的Lamè公式。     

圆柱正交异性复合厚壁圆筒的弹-塑性分析

本文导出了不可压缩和可压缩材料,平面应变问题的Tsai-Hill屈服准则形式;研究了在均匀径向压力作用下圆柱正交异性复合厚壁圆筒的弹-塑性应力场和位移场.求得了弹性屈服压力、极限载荷和安定载荷的公式.     

基于应变梯度理论的粘塑性厚壁圆筒和球壳极限内压分析

基于应变梯度塑性理论,分析了内压作用下厚壁圆筒和球壳的塑性极限荷载．结果表明:圆筒内径在微米量级时,存在尺度效应现象,内径减小,其尺度效应增强;变形越大,影响越大;应变速率敏感指数越大,尺度效应越明显．经典塑性理论结果是当前解的特例．     

权函数法研究高速旋转厚壁筒的应力强度因子

采用厚壁筒在内压作用下的应力强度因子作为参考载荷的应力强度因子,通过权函数方法推导出了内壁带二维径向边裂纹的旋转厚壁筒的应力强度因子公式．这些公式可用于计算旋转厚壁筒在不同裂纹深度、转速、材料和尺寸情况下的应力强度因子．算例表明该文的公式具有良好的精度．同时还研究了旋转圆筒应力强度因子随裂纹深度和内外径比之间的变化规律,方便了工程应用．     

高温高压模拟井筒应力分析与评价

模拟井筒是用于模拟油田井下高温高压环境的实验装置，为高温高压厚壁容器.基于热力学及大涡模拟(LES)理论，建立了模拟井筒温度场物理方程.基于热弹性力学理论，建立了热应力物理方程.采用投影法求解温度场控制方程，采用梯形法数值积分求解热应力控制方程，给出了控制方程的离散格式.通过虚拟密度法对流固耦合传热进行求解，根据应力叠加原理对模拟井筒热应力和压应力及其耦合作用进行了数值求解分析.研究结果表明：设计壁厚最小值为0.18 m的模拟井筒，强度能够满足在400℃加热环境、内部加压220 MPa工作参数下进行高温高压实验.通过实验验证了所建立的数学模型与数值求解方法的正确性，为高温高压厚壁容器设计提供了理论依据.     

具界面损伤压电智能层合板的非线性自由振动分析

基于广义6自由度板理论、应变等效原理和Hamilton变分原理,通过引入三维弹性平衡方程和静电平衡方程的通解来构造满足界面间力电耦合关系和各类连续条件的位移、电势分布形函数,建立了具铺设层内和层间界面处损伤效应的压电智能层合板的非线性运动控制方程组,并运用Galerkin 方法进行求解.数值算例中,分别讨论了,不同损伤程度、压电层厚度、厚跨比及长宽比对四边简支非理想界面压电智能层合板线性自由振动频率和非线性幅频响应曲线的影响.     

采用新方法研究加层压电材料中平行界面共线双裂纹的断裂问题

利用新的方法(Schmidt方法)研究加层压电材料中含共线并与材料界面平行的双裂纹在稳态弹性波作用下的动态问题,经富立叶变换使问题的求解转换为求解两对三重对偶积分方程.这些方程可以采用Schmidt方法来求解,这个方法不同与以前求解所利用的方法.结果表明应力强度因子不仅与裂纹的几何尺寸、入射波频率、加层厚度有关,而且与材料性质有关.     

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．     

Torsional wave dispersion relations in a pre-stressed bi-material compounded cylinder with an imperfect interface

This paper studies the influence of the imperfectness of the contact condition on the torsional wave propagation in the initially stressed (stretched) bi-material compounded circular cylinder. The investigation is carried out within the scope of the piecewise homogeneous body model with the use of the Three-dimensional Linearized Theory of Elastic Waves in Initially Stresses Bodies. The mathematical formulation of the corresponding eigen-value problem is formulated and the solution method for that is developed. The two cases considered are the bi-material compounded cylinder consists of the solid inner and surrounding hollow outer cylinders (Case 1); the bi-material compounded cylinder consists of the hollow inner and surrounding hollow outer cylinders (Case 2). The mechanical relations of the cylinders’ materials are written through the Murnaghan potential. It is proven that the imperfectness of the contact condition does not influence the asymptotic-limit values of the wave propagation velocity. Moreover, the numerical results on the effects of the imperfectness of the boundary condition on the influence of the initial stresses on the wave propagation velocity are presented and discussed.     

A Theoretical Model and Experimental Investigation of a Nonlinear Constitutive Equation for Elastic Porous Metal Rubbers

Starting from the theory of porous materials, the nonlinear theory of dry friction, and the model of a bent slender beam, a nonlinear constitutive equation for elastic porous metal rubbers is constructed. Static compressive experiments were carried out on hollow cylinders of such a rubber, from which relations between all coefficients of the constitutive equation and the material density were determined. Based on the data obtained, the constitutive equation of the material was predicted successfully. The effect of density of the metal rubber on its stiffness and on the nonlinear constitutive equation was revealed by experiments.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 4, pp. 449–460, July–August, 2005.     

压电弹性动力学中第二类Volterra积分方程的数值解法

对于径向变形的压电空心圆柱和空心球弹性动力学问题,丁皓江等最近的研究表明,可以将它转变为关于一个时间函数的第二类Volterra积分方程,使求解工作得到极大的简化,又使探索第二类Volterra积分方程的快速而又高精度的数值解法成为一个关键．采用插值逼近方法,成功地导出了两个新型的递推公式,不仅计算速度快,且在较大时间步长时仍具有足够的精度,有着广泛的应用价值．     

An analytical method for magnetothermoelastic analysis of functionally graded hollow cylinders

This paper considers magnetothermoelastic behavior of a functionally graded material (FGM) hollow cylinder, placed in a uniform magnetic field, subjected to thermal and mechanical loads. Exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow cylinders is determined by using the infinitesimal theory of magnetothermoelasticity. Numerical results indicate that the inhomogeneous constants presented in the present study are useful parameters from a design point of view in that it can be tailored for specific applications to control the stress and perturbation of magnetic field vector distributions. This research is helpful for the optimum design annular cylindrical FGM sensors/actuators.     

Flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders in the presence of magnetic field

In this paper, the flow field of a third-grade non-Newtonian fluid in the annulus of rotating concentric cylinders has been investigated in the presence of magnetic field. For this purpose, the constitutive equation of such a fluid flow was simplified, and the existence of the solution to the governing equation was established using Schauder's fixed point theorem. Using the finite difference method, the numerical solution of the non-dimensionalized form of the established governing equation was obtained. The effect of sundry parameters such as the rotating speed of the cylinders, the physical properties of fluid, and magnetic field intensity on the fluid velocity field was studied as well.     

Interaction of a hollow cylinder of finite length and a plate with a cylindrical cavity with a rigid insert

Two problems of the interaction of a hollow circular cylinder with load-free ends and an unbounded plate with a cylindrical cavity and a symmetrically imbedded rigid insert are considered. Homogeneous solutions are found and the generalized orthogonality of these solutions is used when the modified boundary conditions are satisfied. As a result, we have a system of two integral equations in functions of the displacements of the outer and inner surfaces of the hollow cylinder. These functions are sought in the form of sums of a trigonometric series and a power function with a root singularity. The ill-posed infinite systems of linear algebraic equations obtained are regularized by the introduction of small positive parameters. Since the elements of the matrices of the systems as well as the contact stresses are defined by poorly converging numerical and functional series, an efficient method for calculating of the remainders of the above-mentioned series is developed. Formulae are found for the contact pressure distribution function and the integral characteristic. Examples of the calculation of the interaction of the cylinder and the plate with an insert are given.The method of solving contact problems described here has been used earlier1, 2 and the generalized orthogonality of the solutions found for bodies of finite dimensions, that is, for a rectangle and cylinders of finite length, is its basis. Problems for hollow cylinders with a band ² and an insert reduce to a system of two integral equations, and the problem for a rectangle¹ reduces to one integral equation. Solving these integral equations, ill-posed systems of linear algebraic equations are obtained which are subject to regularization³.     

Comparison of analytical and numerical methods for homogenization of nanotube-reinforced polymers

Carbon nanotubes are increasingly getting impact as reinforcing material for polymer based nanocomposites. Hence, new modeling strategies are necessary to calculate the behavior of these materials. In the last years some attempts have been made using and developing classical micromechanical models. On the other hand numerical homogenization methods are available to tackle this problem. Examples for both types of modeling strategies are presented with focus on the nanotube geometry. The nanotubes are modeled as hollow tubes as well as as isotropic and transversely isotropic cylinders. As expected the results of numerical and analytical methods are identical for isotropic cylinder inclusions. Small deviations occur for transversely isotropic cylinders in transverse direction. In the case of hollow tube inclusions, the analytical models lead to lower stiffness values in transverse direction and for shear. The largest deviations occur for longitudinal shear with magnitudes smaller than 10%. In contrast the effort to get numerical results is enormous, so that the analytical models are still useful. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration analysis of a rigidly fixed viscothermoelastic hollow sphere

In this paper an exact analysis of homogenous rigidly fixed vibrations of viscothermoelastic hollow sphere is presented. The basic governing partial differential equations have been reduced to ordinary differential equations by using Helmholtz decomposition equations. The uncoupled equation is taken for first class vibrations and remains independent of temperature variations, while coupled system of equations are taken for second class vibrations. Matrix Fröbenious method of extended power series has been applied in the coupled system of differential equations to get displacements and temperature. Numerical results have been presented, giving lowest frequency, dissipation factor, displacements and temperature change.