实心球体在热冲击下的动应力和某些现象

本文提出一种简便的解析方法求解实心球体在热冲击载荷作用下的动应力响应。从热动应力的解析表达式和计算结果可以发现圆心处的动应力具有动应力集中现象,并且随着应力波在球体外边界的不断反射而产生周期性振荡。     

高速云纹摄影的一些应用

云纹法与高速摄影相结合是解决动态力学量测量的有效手段之一。本文介绍了高速云纹摄影在动态应变场测量、应力波波形及速度测量、动态应力集中现象、动态断裂问题等方面的应用。     

热超弹性材料中的空穴生成问题

研究热超弹性材料中的空穴生成问题,讨论了温度对空穴生成的影响．球体的材料为考虑温度影响的不可压Gent-Thomas材料,或者说是一种与不可压Gent—Thomas材料对应的热超弹性材料,得到了在表面死载荷作用下球体中空穴生成时的分叉曲线及临界载荷,给出了球体中的应力分布,讨论了温度对临界载荷、分叉曲线和应力分布的影响。     

表面润湿性对球体斜射入水过程的影响研究

针对球体表面润湿性对倾斜入水空泡演化过程及球体动力特性的影响开展研究,以便能够进一步理解润湿性对入水过程的影响并且能够为多种情况下的入水现象提供理论依据.基于球体入水过程空泡形态观察、采集与测量实验平台,分析了亲水性和疏水性球体入水过程中入水喷溅和空泡的演变规律,并深入讨论了不同速度下球体表面润湿性对球体入水过程中动力特性的影响.研究表明,不同表面润湿性球体在入水过程中的喷溅及入水空泡演化与动力特性存在明显区别.在相同入水速度下,亲水性球体的三相接触点远高于疏水性球体,而喷溅的高度却低于疏水性球体,但该差异随入水速度的增加反而减小.随着入水速度的增大,亲水性球体依次经历了无空泡、浅闭合和面闭合3种闭合方式,而疏水性球体先后只出现了深闭合和面闭合两种.但是,随着入水速度的增加,球体表面润湿性对空泡演化过程的影响逐渐减弱,当速度增加到11.25 m/s时,二者不存在区别.同时发现,在入水过程中,在相同速度下生成入水空泡较无入水空泡其总流动阻力系数降低49.94%;亲水性球体生成空泡体积更小,空泡带来的附加质量力也更小,减阻效果更好.     

求解应力集中系数的材料力学方法

采用圣维南原理及曲杆应力公式对U形缺口受拉板条的应力集中系数进行了分析,其结果与有限元解基本吻合。在材料力学教学中,利用材料力学方法推导出应力集中系数,将使学生更好地理解应力集中现象及圣维南原理。     

可压超弹性-塑性材料中的空穴生成

本文研究了材料的弹塑性性质对球体中空穴生成问题的影响，材料的弹性用一种可压超弹性材料的本构关系来描述，材料的塑性用满足材料的不可压条件和Tresca屈服条件的理想塑性材料的本构关系来描述。这类超弹性．塑性材料中可以发生空穴的生成现象，得到了在表面拉伸作用下球体中空穴生成时空穴半径与临界拉伸之间的关系式和临界拉伸。球体的变形可分为弹-塑性变形阶段和完全塑性变形阶段，球体中心首先形成塑性变形区域，并有空穴的突然生成；塑性变形区域能够快速增长，并且使球体很快进入完全塑性变形阶段；空穴在弹-塑性变形阶段迅速增长，但进入完全塑性变形阶段后增长较慢。同时给出了不同变形阶段球体中的应力分布。数值结果表明材料的塑性性质对材料中的空穴生成有明显的影响。     

一种测试动态应力集中的灰色建模方法

将灰色系统方法理论中的GM（1,1）模型,应用于动态应力集中测试的数据处理,根据应力集中处附近的应变测试值,能方便地求出应力集中处的最大应变值。结果表明,该方法简单,预测精度较高,应用方便。     

应力波在缺口处绕射传播的实验研究

本文采用动光弹技术对应力波遭遇到缺口边界时的绕射传播现象进行了初步实验研究，并对所产生的应力集中及动态断裂进行了半定量分析，本文研究可供目前广泛采用的控制爆破法拆除旧建筑物和废设备基础的工作提供参考。     

第三型应变时效的提出与研究进展

第三型应变时效现象的发现使得传统的对于金属塑性流动行为的认识、位错的热激活理论以及常见的金属热粘塑性本构模型均需要进一步完善。为了系统地认识第三型应变时效,首先介绍了第三型应变时效现象区别于静态应变时效和Portevin-Le Chatelie动态应变时效的宏观特征,其次,对第三型应变时效的微观机理以及第三型应变时效与Portevin-Le Chatelier动态应变时效、蓝脆现象以及机械波谱的关联性进行了系统总结。最后,介绍了包含第三型应变时效的金属热黏塑性本构模型的发展。     

2021-05期目录

第三型应变时效现象的发现使得传统的对于金属塑性流动行为的认识、位错的热激活理论以及常见的金属热粘塑性本构模型均需要进一步完善.为了系统地认识第三型应变时效,首先介绍了第三型应变时效现象区别于静态应变时效和Portevin-Le Chatelie动态应变时效的宏观特征,其次,对第三型应变时效的微观机理以及第三型应变时效与Portevin-LeChatelier动态应变时效、蓝脆现象以及机械波谱的关联性进行了系统总结.最后,介绍了包含第三型应变时效的金属热黏塑性本构模型的发展.     

The elastodynamic solution for a solid sphere and dynamic stress-focusing phenomenon

This paper presents an analytical method of solving the elastodynamic problem of a solid sphere.The basic solution of the elastodynamic problem is decomposed into a quasi-static solution satisfying the inhomogeneous compound boundary conditions and a dynamic solution satisfying the homogeneous compound boundary conditions.By utilizing the variable transform,the dynamic equation may be transformed into Bassel equation.By defining a finite Hankel transform,we can easily obtain the dynamic solution for the inhomogeneous dynamic equation.Thereby,the exact elastodynamic solution for a solid sphere can be obtained.From results carried out,we have observed that there exists the dynamic stress-focusing phenomenon at the center of a solid sphere under shock load and it results in very high dynamic stress-peak.     

Analytical thermo-elastodynamic solutions for a nonhomogeneous transversely isotropic hollow sphere

Summary  The spherically symmetric dynamic thermoelastic problem for a special nonhomogeneous transversely isotropic elastic hollow sphere is formulated by introduction of a dependent variable and separation of variables technique. The derived solution can be degenerated into that for a homogeneous transversely isotropic hollow sphere, a nonhomogeneous isotropic hollow sphere or a solid sphere. The present method, allow to avoid integral transforms, is suited for a hollow sphere of arbitrary thickness subjected to arbitrary spherical symmetric thermal and mechanical loads, and is convenient in dealing with different boundary conditions of dynamic thermoelasticity . The numerical calculation involved is easy to be performed and its results are also presented. Received 30 October 2001; accepted for publication 21 February 2002 The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016)     

Transient responses of a multilayered spherically isotropic piezoelectric hollow sphere

The dynamic solution of a multilayered spherically isotropic piezoelectric hollow sphere subjected to radial dynamic loads 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 method of separation of variables coupled with the initial parameter method as well as the orthogonal expansion technique. By using the quasi-static and dynamic parts, 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 spherically isotropic piezoelectric hollow sphere consisting of arbitrary layers and subjected to arbitrary spherically symmetric dynamic loads. Finally, numerical results are presented and discussed.     

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.     

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)     

热冲击载荷作用下的含球形空腔的广义热弹性功能梯度球形各向同性体

This paper is concerned with the determination of thermoelastic displacement, stress and temperature in a functionally graded spherically isotropic infinite elastic medium having a spherical cavity, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters （Green and Lindsay theory）. The surface of cavity is stress-free and is subjected to a time-dependent thermal shock. The basic equations have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by an eigenvalue approach. Numerical inversion of the transforms is carried out using the Bellman method. Displacement, stress and temperature are computed and presented graphically. It is found that variation in the thermo-physical properties of a material strongly influences the response to loading. A comparative study with a corresponding homogeneous material is also made.     

Exact Electromagnetothermoelastic Solution for a Transversely Isotropic Piezoelectric Hollow Sphere Subjected to Arbitrary Thermal Shock

This paper presents analytical study for electromagnetothermoelastic transient behavior of a transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Exact solutions for the transient responses of stresses, perturbation of magnetic field vector, electric displacement and electric potential in the transversely isotropic piezoelectric hollow sphere are obtained by means of the Hankel transform, the Laplace transform and their inverse transforms. An interpolation method is used to solve the Volterra integral equation of the second kind caused by interactions among electric, magnetic, thermal and elastic fields. From the sample numerical calculations, it is seen that the present method is suitable for the transversely isotropic hollow sphere, placed in a uniform magnetic field, subjected to arbitrary thermal shock. Finally, the result can be used as a reference to solve other transient coupling problems of electromagnetothermoelasticity.     

Dynamic thermal shock in a layered cylinder with initial interface pressure

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Transient responses of a magneto-electro-elastic hollow sphere for fully coupled spherically symmetric problem

By introducing a dependent variable and a special function satisfying the inhomogeneous mechanical boundary conditions, the governing equation for a new variable with homogeneous mechanical boundary conditions is derived. Then by means of the separation of variables technique and the electric and magnetic boundary conditions, the dynamic problem of a magneto-electro-elastic hollow sphere under spherically symmetric deformation is transformed to two Volterra integral equations of the second kind about two functions of time. Cubic Hermite polynomials are adopted to approximate the two undetermined functions at each time subinterval and the recursive formula is obtained to solve the integral equations successfully. The transient responses of displacements, stresses, electric and magnetic potentials are completely determined at the end. Numerical results are presented.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.