Elastodynamic solution of a non-homogeneous orthotropic hollow cylinder

A theoretical method for analyzing the axisymmetric plane strain elastodynamic problem of a non-homogeneous orthotropic hollow cylinder is developed. Firstly, a new dependent variable is introduced to rewrite the governing equation, the boundary conditions and the initial conditions. Secondly, a special function is introduced to transform the inhomogeneous boundary conditions to homogeneous ones. By virtue of the orthogonal expansion technique, the equation with respect to the time variable is derived, of which the solution can be obtained. The displacement solution is finally obtained, which can be degenerated in a rather straightforward way into the solution for a homogeneous orthotropic hollow cylinder and isotropic solid cylinder as well as that for a non-homogeneous isotropic hollow cylinder. Using the present method, integral transform can be avoided and it can be used for hollow cylinders with arbitrary thickness and subjected to arbitrary dynamic loads. Numerical results are presented for a non-homogeneous orthotropic hollow cylinder subjected to dynamic internal pressure. The project supported by the National Natural Science Foundation of China (10172075 and 10002016)     

Dynamic behavior of piezoelectric/magnetostrictive composite hollow cylinder

The dynamic behavior of a multilayered, perfectly bonded piezoelectric/magnetostrictive composite hollow cylinder under radial deformation is investigated. The superposition method, the state space method as well as the separation of variables method are elegantly integrated in the solution approach. The governing equations are finally transformed into two Volterra integral equations of the second kind with respect to two functions of time. The elastic, electric and magnetic fields are finally obtained according to solving the integral equations. Free vibrations and transient responses are demonstrated by numerical experiments.     

Stress analysis of circumferentially corrugated hollow orthotropic cylinders

A problem-solving approach based on discrete Fourier series is used to analyze the stress state of corrugated orthotropic and transversely isotropic hollow cylinders __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 12, pp. 87–96, December, 2006.     

Dynamic solution of a multilayered orthotropic piezoelectric hollow cylinder for axisymmetric plane strain problems

The dynamic solution of a multilayered orthotropic piezoelectric infinite hollow cylinder in the state of axisymmetric plane strain is obtained. By the method of superposition, the solution is divided into two parts: one is quasi-static and the other is dynamic. The quasi-static part is derived by the state space method, and the dynamic part is obtained by the separation of variables method coupled with the initial parameter method as well as the orthogonal expansion technique. By using the obtained quasi-static and dynamic parts and the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials are finally obtained. The present method is suitable for a multilayered orthotropic piezoelectric infinite hollow cylinder consisting of arbitrary layers and subjected to arbitrary axisymmetric dynamic loads. Numerical results are finally presented and discussed.     

Transient response of a finite crack in an orthotropic strip under the in-plane shear impact

The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor near the crack tip is derived. Numerical results of with in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace transform.     

Axisymmetric smooth contact for an elastic isotropic infinite hollow cylinder compressed by an outer rigid ring with circular profile

A contact problem for an infinitely long hollow cylinder is considered. The cylinder is compressed by an outer rigid ring with a circular profile. The material of the cylinder is linearly elastic and isotropic. The extent of the contact region and the pressure distribution are sought. Governing equations of the elasticity theory for the axisymmetric problem in cylindrical coordinates are solved by Fourier transforms and general expressions for the displacements are obtained. Using the boundary conditions, the formulation is reduced to a singular integral equation. This equation is solved by using the Gaussian quadrature. Then the pressure distribution on the contact region is determined. Numerical results for the contact pressure and the distance characterizing the contact area are given in graphical form. The English text was polished by Yunming Chen     

Nonstationary heat transfer in a hollow composite cylinder

Solution of a nonstationary heat-transfer problem for bounded end-conjugated hollow dissimilar cylinders is presented. In the volume of the cylinders, time- and coordinate-dependent heat release of known intensity takes place. The problem is solved using finite integral transformations over two coordinates.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 2, pp. 130–140, March–April, 2005.     

An approach to three-dimensional elasticity problem of cylindrical orthotropic bodies

The state equation for a static or dynamic thermal elastic problem of cylindrical orthotropic bodies is derived using the three-dimensional theory of elasticity. The governing equation for displacement components is obtained by series expansion, and for simplicity the case of an axisymmetric problem of transverse isotropic bodies is given. For illustration, an axisymmetric problem of a combined-cylinder made of two transverse isotropic materials is also presented. Some interesting and significant results are obtained.Supported by-National Natural Science Foundation and Post-Doctor's Foundation of China     

Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders

The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions of several types are presented Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 74–85, October 2008.     

热弹性平面问题的规则化边界积分方程

对于热弹性平面问题,过去广泛集中在直接变量边界元法研究,本文研究间接变量规则化边界元法,建立了间接变量规则化边界积分方程。和直接边界元法相比,间接法具有降低密度函数的连续性要求、位移梯度方程中的热载荷体积分具有较弱奇异性等优点。数值实施中,用精确单元描述边界几何,不连续插值函数逼近边界量。算例表明,本文方法效率高,所得数值结果与精确解相当吻合。     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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Transient thermal stresses in two-dimensional functionally graded thick hollow cylinder with finite length

In this paper transient thermal stresses in a thick hollow cylinder with finite length made of two-dimensional functionally graded material (2D-FGM) based on classical theory of thermoelasticity are considered. The volume fraction distribution of materials, geometry and thermal load are assumed to be axisymmetric but not uniform along the axial direction. The finite element method with graded material properties within each element is used to model the structure. Temperature, displacements and stress distributions through the cylinder at different times are investigated. Also the effects of variation of material distribution in two radial and axial directions on the thermal stress distribution and time responses are studied. The achieved results show that using 2D-FGM leads to a more flexible design so that time responses of structure, maximum amplitude of stresses and uniformity of stress distributions can be modified to a required manner by selecting suitable material distribution profiles in two directions.     

实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学解

利用分离变量法,成功地给出了各向同性实心圆柱外表面受热冲击作用的轴对称平面应变热弹性动力学问题的解析解.运用此方法,可以避免积分变换且易于实现数值计算.在数值结果中,与拟静态问题和均匀热冲击情形进行了比较,表明惯性项对中心处应力响应影响不大,而热传导的过程能大大减低中心处的热应力.     

压电空心圆柱中波的传播

应用三维压电弹性体轴对称模型对压电空心圆柱中波的传播进行了研究. 发现在 圆柱中是否具有压电性质会对波的传播带来显著的差异. 当波长趋向于零时，在压电圆柱中 拟P波的波速渐进趋向于横观各向同性弹性体的准P波波速，而非压电圆柱中拟P波的波速 渐进趋向于一维杆模型中的P波波速；在压电圆柱中拟SV波存在驻波现象. 圆柱中的SH波 同电场无关，所以在压电圆柱和非压电圆柱中SH波具有相同的频散曲线. 应用积分变 换方法将圆柱的控制方程同其侧边界条件相结合，得到了一组动力学方程. 针对具体的侧边 界条件，得到相对应的波导条件和频散方程. 在此基础上通过数值计算模拟了圆柱受到端部 应力脉冲激励后的瞬态响应. 同时讨论了空心圆柱的半径比对轴向波传播的影响.     

轴对称热冲击SIF过渡过程分析的热权函数法

热权函数法利用温度与热权函数的乘积的积分来直接计算热冲击过程中裂纹尖端的应力强度因子过渡过程。热权函数与时间τ无关,由于免除了对每一时刻τ所需作的有限元或边界元分析,计算过程大大简化,计算效率得到极大提高,本文将热权函数与有限元法直接耦合,给出了基于刚度阵导数法的轴对称问题的热权函数计算格式,实例计算表明,本文给出的热权函数计算格式具有满意的计算精度。     

层合球面各向同性热释电空心球的瞬态响应

运用叠加原理，将层合球面各向同性热释电空心球的球对称动力学问题的解分成准静态和动 态两部分，准静态部分首先运用状态空间法给出了显式表达式，然后运用分离变量法、初参 数法和特征函数展开技术，给出了动态部分的表示式，再结合内外表面上的电学边界条件和 界面上的电学连续条件，导出一个关于时间函数的第二类Volterra积分方程，运用插值法 可成功地给出此积分方程的高精度数值解，最终可求得原问题的位移、应力、电位移以及电 势的响应. 此方法适用任意层数且各层是任意厚度的层合热释电空心球作用随时间以任意形 式变化的球对称温度场. 文中还给出了数值结果.     

Analysis of transient thermal stress in cylindrically orthotropic tubes

IntroductionCylindricallyorthotropictubesarenowwidelyappliedinengineering ,theresearchofthestressesfieldhasattractedalotofattentionfromscientistsandengineers .ConsiderableworksonstressfieldduetomechanicalloadinghavebeendonebyLehknitskii[1],Sherrer[2 ]andPagano[3].KalamandTauchert[4 ],HyerandCooper[5 ]studiedthethermalstressesinorthotropiccylindersduetosteaky_statetemperaturegradient.TheproblemoftransientthermalstressesinaholloworthotropiccircularcylinderwasfirstlyproposedandtreatedbyKardoma…     

Influence of magnetic field on free vibrations in elastodynamic problem of orthotropic hollow sphere

The effect of magnetic field on the plane vibrations for an elastodynamic orthotropic sphere is studied. Equations of elastodynamic problems of the orthotropic hollow sphere in terms of displacement are solved. The numerical results of the frequency equations in the presence of magnetic field are discussed and shown graphically. Compar-isons are made with the result in the presence and absence of magnetic field in the case of orthotropic sphere. The results show that the effect of magnetic field is very pronounced.     

Control of stress response in a rotating infinite hollow multilayered piezoelectric cylinder

The theoretical study of the control of stress is developed for a rotating infinite hollow multilayered radially polarized piezoelectric cylinder. The exact solution is obtained by means of the state-space method. As an illustrative example, the distribution of the radial and tangential stresses in a rotating hollow internally pressurized five-layered piezoelectric cylinder subjected to different electric potential at the internal and external surfaces are performed. Numerical results show that the distribution of the stress can be controlled by applying appropriate electric potentials at the correct surfaces.