嵌入弹性半空间的弹性迴转轴的扭转*

本文用线载荷积分方程法(LLIEM)研究嵌在弹性半空间的弹性迴转轴的扭转问题.将“点环力偶(PRC)”和“半空间点环力偶(PRCHS)”分别分布于迴转轴内和外的轴线上,就能将本问题归结为一维的Fredholm第一种积分方程组.直接用离散法求解时,会发现有时解是不稳定的,也就是病态情形.本文采用以带小参数的Fredholm第二种积分方程代替病态的Fredholm第一种积分方程的方法可以得到稳定的解,此法比Tikhonov正规化法简单,易于在计算机上运行.文中给出圆维、圆柱、圆锥-圆柱、抛物线轴等数值例子.     

线载荷积分方程法的位移和应力场的唯一性定理

根据Fredholm定理,本文证明了由满足边界条件的分布于弹性体所占的区域之外的虚的基本载荷引起的弹性体所占的区域之内的位移和应力场是唯一的.本定理为线载荷积分方程法的应用奠定理论基础.     

简便积分方程法分析桩

本文用两种方法来分析桩受垂直载荷作用问题.一种是:将由Mindlin集中力组成的轴对称载荷沿弹性半空间z轴的[0,L]内分布,并迭加Boussinesq的解;另一种是:除上述诸虚载荷外,还将Mindlin的垂直集中力沿z轴的[0,L]内分布.前者使边界条件为: 的桩受垂直载荷问题归结为一个Fredholm第一种积分方程;后者使边界条件(其中1,3式同)(0.1)式中的2为:0≤z≤L,U(e,z)=a-e,(e→a);W(a,z)=常数(0.2)的桩受垂直载荷问题归结为两个联立的Fredholm第一种方程式.对刚性桩而言,前者适于容许桩和其侧面附着的土有相对滑动情况;后者适于无相对滑动情形.这两种方法较现有的虚载荷分布于桩表面的诸法具有下列优点:1.所得的积分方程不是二维、奇异的;而是一维、非奇异的.2.能考虑初应力的影响.第一种方法还无须预先假定沉陷函数W;在可压缩桩中容易考虑三维应力的影响的好处.本文还给出Fredholm第一种积分方程近似解误差估计的一个定理,以及两种方法用DJS—21机计算单桩沉陷的结果.     

乏晰边界条件的弹性体静力问题的解和最小位能、余能原理

本文把弹性力学静力问题的解定义在集合论基础上,并推广到乏晰边界条件情形.给出最小位能、余能原理在乏晰边界条件下新的推广,以及最小元位能解的存在和唯一性定理,从而证明弹性力学静力问题的拟解是存在的.     

Pile analysis by simple integral equation methods

Two simple integral equation methods are proposed for the analysis of vertical loaded pile. One of them is; let the axisymmetrical loads formed by Mindlin's horizontal point forces be distributed along the axis z in [0, L] of the elastic half-space, and composed with the Boussinesq's point force. The other is: in addition to the above fictitious loads, the. Mindlin's vertical forces are distributed along the axis z in [0, L]. The former reduces the problem of a vertical loaded pile embedded in a half-space with the following boundary conditions.     

轴对称问题的积分方程的迭代解法

将集度分别为x(ξ)和y(ξ)的集中力和挤压中心沿物体外弹性空间z轴分布,并迭加应力为常数项的解,就能使轴对称应力问题归结为两个联立的一维Fredholm第一种积分方程,本文研究此类方程的迭代解法.给出与E.Rakotch收缩映射定理等价的引理和迭代收敛证明.     

包含—受扭迴转轴的半空间的性质*

本文研究包含有一根部份嵌入的迴转轴的半空间的性质.不用知道一给定的嵌入的轴的扭转问题的精确解,这些性质能指出此半空间的位移或应力场的某些特点并且有时可以用来检查数值解.文中给出嵌入半空间的受扭的刚性圆柱的轴的表面上的正确的应力分布的检查的例子.     

Solution of simultaneous equations of cosine law arising from subjectivity geometry

This paper discusses the solution of a group of two-order six elements rootedalgebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry^[1]. By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations. Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods. A numerical example by descent method is given.Supported by Scientific Foundation of South China Unviersity of Technology. Ben Xiu-ming took part in the calculation.     

Torsion of elastic shaft of revolution embedded in an elastic half space

The problem of torsion of elastic shaft of revolution embedded in an elastic half space is studied by the Line-Loaded Integral Equation Method (LLIEM). The problem is reduced to a pair of one-dimensional Fredholm integral equations of the first kind due to the distributions of the fictitious loads "Point Ring Couple (PRC) "and "Point Ring Couple in Half Space (PRCHS) "on the axis of symmetry in the interior and external ranges of the shaft occutied respectively. The direct discrete solution of this integral equations may be unstable, i.e. an ill-posed case occurs. In this paper, such an ill-posed Fredholm integral equation of first kind is replaced by a Fredholm integral equation of the second kind with small parameter, which provides a stable solution. This method is simpler and easier to carry out on a computer than the Tikhonov’s regularization method for ill-posed problems. Numerical examples for conical, cylindrical, conical-cylindrical, and parabolic shafts are given.     

Torsion of rigid circular shaft of varying diameter embedded in an elastic half space

The axially symmetric torsion of rigid circular shaft of varying diameter embedded in an elastic half space is studied by line-loaded integral equation method (LLIEM), where the problem is formulated by distributions of ficitious fundamental loads PRCHS (point ring couple in half space) along the axis of symmetry in interval of the shaft and is reduced to a one-dimensional and non-singular Fredholm integral equation of the first kind and is easily solved numerically. Numerical examples of torsin of rigid conic, cylinder, conical-cylinder embedded in an elastic half space are given and compared with the known result obtained by the others. The exact solution of torsion of rigid half sphere embedded in an elastic half space is also presented. Project Supported by the National Science Foundation of China.