泊松方程中域积分化为边界积分的方法

本文讨论了二维和三维泊松方程中域积分化为边界积分的方法。对于形如x~ig_x(y,z)、y~ig_x(x,z)和z~ig_z(x,y)的荷载给出了域积分转化为边界积分的正确公式。而对于复杂荷载,利用泰勒展开将域积分近似地转化为边界积分并给出了误差估计。计算结果表明利用本文方法可大大节省计算时间。因此,本文方法是一种十分有效的方法。     

一类三维随机动力系统的最大Lyapunov指数

基于一维扩散过程的奇异边界理论,使用摄动方法研究了白噪声参激的一类余维二分岔系统的最大Lyapunov指数渐近表达式和数值解,主要讨论了一维相扩散过程同时存在两类奇异边界以及FPK方程存在平稳解的一般性条件. 通过对参激噪声作用项系数矩阵的分析,给出了不变测度的解析解及其相应的Monte Carlo数值仿真结果,并导出了一维相扩散过程P分岔点的确定方法. 对于一类特殊情形,给出了最大Lyapunov指数的渐近表达式;对于参激噪声作用项系数矩阵的一般情形,则给出了系统最大Lyapunov指数的数值结果.      

弹性约束的周期性圆形薄板自由振动分析

采用边界摄动方法对周期性圆形薄板在弹性约束条件下的基频进行了分析,给出了其解析解.基于薄板基本控制方程,以表征边界形状的半径的微小变化量为摄动参数,将挠度和频率摄动展开,获得各阶摄动边值问题的无量纲控制方程和边界条件方程.求解获得确定基频的表达式.通过算例分析阐述了不同的边界波纹圆数,摄动参数及边界转角约束系数对基频的影响规律.通过算例分析阐述了不同的波纹圆数,半径的微小变化量及边界转角约束参数对基频的影响规律.特别地,对于经典边界条件,通过与已有解的比较,验证了结果的正确性.本文解对于较精确分析具有曲线边界的薄板固有频率具有重要指导意义.     

预应力条件下轴对称圆板的响应解

本文研究预应力条件下轴对称简支和固支圆板的瞬态响应,利用振型展开和Laplace变换给出解析表达式,提出简化型圆板的边界条件,利用Hankel变换和Laplace变换给出简捷的解,针对几种边界状态,比较了其频率和响应,同时讨论了几种常见的瞬态载荷的结构响应形式。     

杆中弹塑性边界传播速度的确定

本文在作者以前发表的一篇文章的基础上,给出了加载边界上屈服条件的数学表达式,研究了在一般情况下确定弹塑性边界传播速度的方法,讨论了在弹塑性边界上的折点和杆端可能出现的各种复杂情况,指明了相应的封闭的定解方程组。所得结果是解决具有复杂加载和卸载过程时杆中弹塑性波传播问题的基础,可以作为处理弹塑性边界,特别是有关初始传播速度及折点问题的依据。     

磁-电-弹性半空间在轴对称热载荷作用下的三维问题研究

考虑力-电-磁-热等多场耦合作用, 基于线性理论给出了磁-电-弹性半空间在表面轴对称温度载荷作用下的热-磁-电-弹性分析, 并得到了问题的解析解. 利用Hankel 积分变换法求解了磁-电-弹性材料中的热传导及控制方程, 讨论了在磁-电-弹性半空间在边界表面上作用局部热载荷时的混合边值问题, 利用积分变换和积分方程技术, 通过在边界表面上施加应力自由及磁-电开路条件, 推导得到了磁-电-弹性半空间中位移、电势及磁势的积分形式的表达式. 获得了磁-电-弹性半空间中温度场的解析表达式并且给出了应力, 电位移和磁通量的解析解. 数值计算结果表明温度载荷对磁-电-弹性场的分布有显著影响. 当温度载荷作用的圆域半径增大时, 最大正应力发生的位置会远离半无限大体的边界; 反之当温度载荷作用的圆域半径减小时, 最大应力发生的位置会靠近半无限大体的边界. 电场和磁场在温度载荷作用的圆域内在边界表面附近有明显的强化, 而磁-电-弹性场强化区域的强化程度跟温度载荷的大小和作用区域大小相关. 本研究的相关结果对智能材料和结构在热载荷作用下的设计和制造具有指导意义.      

计入横向剪切变形平板弯曲的边界元素法

基于具有三个广义位移的板弯曲理论,本文导出仅含三角函数和对数1/2阶的基本解,使用起来较[2]更为方便·利用Betti互易定理,得出边界积分方程.在边界上的内力和位移均离散为常量场,并给出了在奇异积分单元上奇异积分的全部解析表达式.文末的两个算例表明,无论对厚板还是薄板,本文提出的边界元素法均给出较满意的结果.     

回转体弹塑性扭转问题的一种边界积分方程解法

本文利用调和函数性质和格林公式,建立以应力函数和边界合剪应力为场变量的边界积分方程.对奇异积分,按离开奇异点远近不同分别采用不同阶次的高斯积分.处理了角点处五种可能的情况和零轴上积分分母为零的现象.对于弹性和弹塑性问题都给出了部分实例.并与理论解,由Kelvin解建立的边界元法和松弛法作了比较.均得出十分满意的结果.     

压电介质边界元法及奇异性处理

本文从压电材料的基本方程出发,利用功的互等原理推导了边界积分方程,并详细地讨论了边界元的计算步骤,利用等参变换,着重研究了在边界元计算中基本解的奇异性问题,对各种情况讨论了系数矩阵H和G的算法,并给出院具体的表达式,作为算例,选取了均匀薄板和开孔薄板PZY-4压电材料,计算结果表明,本文提出的边界元的计算格式和奇异性的处理方法相当有效。     

环形板的非轴对称屈曲分析

本文利用打靶法研究了内外边界固支且在外边界受均匀径向压力作用下的极正交各向异性环形板的非轴对称屈曲和过屈曲,计算了临界载荷,讨论了分支解的存在性,得到了分支解的渐近表达式,分析了环形板的屈曲性态。     

On the general expression of Fredholm Integral Equations Method in elasticity

In this paper, the concept of covering domain is introduced to develop a general expression for the Fredholm Integral Equations Method, by which elasticity problems of arbitrarily shaped bodies loaded by external forces can be solved. Some special expressions are given for a body with non-zero remote stresses, or subjected to some concentrated forces on its boundary. The relationship between the loading forces and solutions are also discussed. Some analytical solutions can be obtained for simple cases. When numerical computations are needed for the solution, the method proves to have high precision and fast convergency.     

Exact solution of a semi-infinite crack in an infinite piezoelectric body

Summary The paper presents an exact and complete solution of the problem of a semi-infinite plane crack in an infinite transversely isotropic piezoelectric body. The upper and lower crack faces are assumed to be loaded symmetrically by a couple of normal point forces in opposite directions and a couple of point charges. The solution is derived through a limiting procedure from the one of a penny-shaped crack. The expressions for the elastoelectric field are given in terms of elementary functions. Received 10 August 1998; accepted for publication 18 November 1998     

GENERAL SOLUTION OF PLANE PROBLEM OF PIEZOELECTRIC MEDIA EXPRESSED BY "HARMONIC FUNCTIONS

I.IntroductionBecauseofthecouplingcharacteristicbetweenthemechanicaldeformationandthee1ectricaleffect,piezoelectricmaterialshavebeenwidelyusedintransducersandsmartstructures.Moreandmoreattentionshavebeenpaidonsuchmaterials,andgreatadvanceshavebeenmadeinva…     

移动接触下求解二维闭合裂纹的双重迭代边界元法

使用子域边界元法对受移动接触弹性体作用下的二维闭合裂纹问题进行了数值计算。由于两弹性体的接触界面和裂纹表面的接触范围的大小和接触状态事先是未知的 ,对此 ,在两个接触表面同时采用迭代的方法进行了求解。在裂纹的每个裂尖上都采用了四分之一的奇异单元以保证裂尖位移场和应力场奇异性的满足。用我们编制的二维裂纹问题程序对一些中心裂纹问题进行了计算 ,计算结果与经典断裂力学的理论值比较吻合。在无摩擦的条件下 ,对一些具有不同角度且受移动接触弹性体作用下的闭合裂纹问题进行了数值计算 ,得到了一些耦合作用下的应力强度因子的计算结果     

A penny shaped crack in a transversely isotropic material under non-axisymmetric impact loads

A solution is given for problems involving non-axisymmetric dynamic impact loading of a penny shaped crack in a transversely isotropic medium. Laplace and Hankel transforms are used to reduce the equations of elasticity to integral equations, and solutions are obtained for the three modes of fracture. The stress intensity factors are determined for a penny shaped crack loaded by concentrated normal impact forces and concentrated radial shear impact forces. The integral equations are solved by numerical methods, and the results are plotted showing how the dynamic stress intensity factors are influenced by the asymmetric loading.     

Study for 2D moving contact elastic body with closed crack using BEM

Using a sub-regional boundary element method, an algorithm for the two-dimensional elastic bodies with a closed crack loaded by a moving contact elastic body is proposed. Since the extent and status of the contact surface of two elastic bodies and the crack within the body are all not known in advance, a double iterative contact algorithm is used. The BEM program for solving the closed crack problems is developed, some numerical examples are calculated, and the results of the center crack cases are shown to be in good agreement with the analytical solution in the classical fracture mechanics. In the condition of friction and non-friction, some coupling computational results of the SIF for the closed crack, with different angles and loaded by a moving contact elastic body, are also obtained by a numerical computation. The project supported by the National Natural Science Foundation of China (10172053) and NJTU Foundation of China (PD-157)     

Semiclosed-form solution for static nonlinear analysis of extensible cables

The analysis of a cable deforming under statically applied body forces leads to a series of differential equations that are inherently nonlinear due to coupling of geometry and loading. These equations have been solved by nonlinear finite element technique, finite difference formulation, or a two-step shooting method. However, a semiclosed-form solution is presented herein in which the governing differential equations are integrated to yield exact expressions for the unknown cable forces and the parameters defining the geometry of the loaded cable. The formulation presented herein is capable of taking care of the large sag and deformation in the cable without employing any numerical solution procedure.     

Development of a solution method for frictional contact problems with complex loading

In this work, solution methods for frictional contact problems are extended to the case of moving punches and to the external loading history-dependent system states. To solve the frictional contact problems in the contact area, an iterative method is developed and implemented. Solutions of two-dimensional problems are constructed using the boundary element method. Numerical analysis is aimed at the quantitative study of effects such as the interaction of contact pressure and friction forces, estimates of the friction force differences due to the differences in the choice of local basis for the calculation of normal pressure and friction forces, and evaluation of the effects of complex loading (rotation of the rigid punch after its preliminary penetration into the solid). We find that, for the same definition of the friction force, different initial approximations lead to the same solution. At the same time, the friction forces defined either as projections onto the common tangent plane or as projections onto the plane tangent to the punch can differ quite substantially. Similar conclusions are derived for the solutions corresponding to single or multiple loading steps. The work relies on the variational principle for the solution of contact problems and numerical algorithms developed for the problems with one-sided constraints. The variational principle was first applied by Signorini [1] to the determination of the stress-strain state in a linearly deformed body in a rigid smooth shell. The modern view of the problem and its generalizations to the frictional problems and some other problems involving unilateral constraints in given in the monograph [2]. Finite difference and finite element methods in application to the problems with unilateral constraints are described in [3]. Analytical solution methods are developed in the monographs [4–6].     

EXACT SOLUTION TO THE PROBLEM OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC BODY SUBJECTED TO ANTISYMMETRIC TANGENTIAL POINT FORCES

An exact and complete solution of the problem of a half-plane crack in an infinite transversely isotropic piezoelectric body is presented. The upper and lower crack faces are assumed to be loaded antisymmetrically by a couple of tangential point forces in opposite directions. The solution is derived through a limiting procedure from that of a penny-shaped crack. The expressions for the electroelastic field are given in terms of elementary functions. Finally, the numerical results of the second and third mode stress intensity factorsk ₂ andk ₃ of piezoelectric materials and elastic materials are compared in figures. Project supported by the National Natural Science Foundation of China (No. 19872060 and 69982009) and the Postdoctoral Foundation of China.