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1.
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 总被引:1,自引:0,他引:1
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. 相似文献
2.
将三维热权函数法扩展为适用于表面力、体积力和温度载荷的通用权函数法(UWF).推导出以变分型积分方程表达的UWF法基本方程,从变分的角度,将求解三维热权函数法基本方程的多虚拟裂纹扩展法(MVCE)改造为可以适用于一般的变分型积分方程的一类新型数值方法--有限变分法(FVM).在FVM中可以引入无穷多种线性无关的局部变分模式,可以根据计算要求在求解域中插入任意多个计算节点,单一型裂纹问题FVM所得到的最终方程组的系数矩阵总是一个对称的窄带矩阵,而且对角元总是大数,具有良好的数值计算性能.FVM对于SIF沿裂纹前缘急剧变化的复杂情况具有较好的数值模拟能力和较高的计算精度,利用自身一致性,可以求得三维裂纹前缘SIF的高精度解. 相似文献
3.
横观各向同性材料的三维断裂力学问题 总被引:4,自引:0,他引:4
从三维横观各向同性材料弹性力学理论出发,
使用Hadamard有限部积分概念, 导出了三维状态下单位位移间断(位错)集度的基
本解. 在此基础上, 进一步运用极限理论, 将任意载荷作用下, 三维无限大横观各向
同性材料弹性体中, 含有一个位于弹性对称面内的任意形状的片状裂纹问题, 归结为求
解一组超奇异积分方程的问题. 通过二维超奇异积分的主部分析方法,
精确地求得了裂纹前沿光滑点附近的应力奇异指数和奇异应力场,
从而找到了以裂纹表面位移间断表示的应力强度因子表达式及裂纹局部扩展所提供
的能量释放率. 作为以上理论的实际应用,最后给出了一个圆形片状裂纹问题
的精确解例和一个正方形片状裂纹问题的数值解例.
对受轴对称法向均布载荷作用下圆形片状裂纹问题,
讨论了超奇异积分方程的精确求解方法, 并获得了位移间断和应力强度因子的封闭解,
此结果与现有理论解完全一致. 相似文献
4.
功能梯度热释电材料矩形板的三维精确分析 总被引:17,自引:2,他引:17
对四边简支、接地、等温的功能梯度热释电材料矩形板进行精确三维分析.根据正交各向异性热释电材料基本方程,导出了功能梯度热释电材料的状态方程.假定材料的机械、电学和热学性质沿板厚方向按统一的指数函数形式梯度分布,获得了四边简支、接地和等温的矩形板,在上下表面作用任意的机械荷载、电荷载和热荷载情况下的三维精确解.通过算例,分析了在机械荷载、电荷载和热荷载分别作用下,材料性质的不同梯度变化对平板结构响应的影响.所获得的精确结果可作为评价其他近似方法的标准解答或者作为建立简化的功能梯度热释电材料平板理论的基础。 相似文献
5.
平面应变 Biot 固结的解析层元 总被引:1,自引:0,他引:1
提出用解析层元法有效地解决任意深度单层土的平面应变 Biot 固结问题. 从 Biot 固结问题的控制方程出发, 采用特征值法在 Laplace-Fourier 变换域内推导出一个精确对称的解析层元刚度矩阵. 通过表示单层土广义力和广义位移之间关系的解析层元, 并结合土层的边界条件, 推导出土层任意点的解答; 物理域内的真实解可以通过 Laplace-Fourier 数值逆变换进一步获得. 通过数值计算验证理论的正确性, 研究了土层性质及时间因素对固结的影响.} 相似文献
6.
基于弹性材料的动态基本方程,结合广义Betti-Rayleigh互易等式与时域下的边界积分方程,推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解,将经过主部分析的积分核函数分解为静态和动态部分,其中动态积分核不具有奇异性。在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换,采用配置点法计算超奇异积分,获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序,得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律,数值结果稳定且收敛速度快。 相似文献
7.
用复变函数中的Cauohy积分公式求出了理想弹塑性材料中小范围屈服条件下Ⅲ型裂纹准静态扩展时裂纹线上塑性区尺寸x_p与应力强度因子K_m的关系式。利用这个关系式将Rice[1]根据临界塑性应变准则建立的x_p(l)的积分方程,l为裂纹扩展量,化为阻力曲线K_R(l)的积分方程.采用文献[2]中的方法得到K_R(l)在不同临界塑性应变下的数值解.结果表明K_R随l的增加而单调增加.最后达到裂纹准静态定常扩展所需要的常数值. 相似文献
8.
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10.
基于弹性材料的动态基本方程,结合广义Betti-Rayleigh互易等式与时域下的边界积分方程,推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解,将经过主部分析的积分核函数分解为静态和动态部分,其中动态积分核不具有奇异性。在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换,采用配置点法计算超奇异积分,获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序,得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律,数值结果稳定且收敛速度快。 相似文献
11.
H. M. Wang H. J. Ding Y. M. Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(9):581-599
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. 相似文献
12.
Dynamic analysis of a two-layered elasto-piezoelectric composite hollow sphere under spherically symmetric deformation is developed. An unknown function of time is first introduced in terms of the charge equation of electrostatics and then the governing equations of piezoelectric layer, in which the unknown function of time is involved, are derived. By the method of superposition, the dynamic solution for elastic and piezoelectric layers is divided into quasi-static and dynamic parts. The quasi-static part is treated independently by the state space method and the dynamic part is obtained by the separation of variables method. By virtue of the obtained quasi-static and dynamic parts, a Volterra integral equation of the second kind with respect to the unknown function of time is derived by using the electric boundary conditions for piezoelectric layer. Interpolation method is employed to solve the integral equation efficiently. The transient responses for elastic and electric fields are finally determined. Numerical results are presented and discussed. 相似文献
13.
H. J. Ding H. M. Wang W. Q. Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2002,72(8):545-553
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) 相似文献
14.
《International Journal of Solids and Structures》2005,42(1):85-102
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. 相似文献
15.
H. J. Ding H. M. Wang W. Q. Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,73(1-2):49-62
Summary By introduction of a special dependent variable and separation of variables technique, the electroelastic dynamic problem of a nonhomogeneous, spherically isotropic hollow sphere is transformed to a Volterra integral equation of the second kind about a function of time. The equation can be solved by means of the interpolation method, and the solutions for displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow sphere with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are presented at the end.The work was supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016). 相似文献
16.
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. 相似文献
17.
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. 相似文献
18.
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. 相似文献
19.
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. 相似文献
20.
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) 相似文献