Formulae of force at a point in the interior of a half space with shear modulus linearly varied with depth

According to a lemma and an assumption, this paper prexenis formulae of force at a point in the interior of a half space with Poisson’s ratio v = constant and shear modulus G linearly varied with depth. These formulae can be used as an approximate basic solution when the integral equation method is employed for the analysis of piles and other geotechnical engineering problems.     

受轴向集中压力的椭球体的应力分析

用积分方程法和光弹性方法分析受轴向集中压力的椭球体.在弹性全空间z=-c轴上的[a,∞)和[-a,-∞)区间上,与z=0平面对称地分布集度为X₁(c)=X₁(-c)的集中力、集度为X₂(c)=X₂(-c)的挤压中心,以及迭加一对平行z轴、等值反向、分别作用于z=α及z=-α上的集中力,就能使受轴向集中压力的椭球体问题归结为两个联立的Fredholm第一种积分方程.然后,便能方便地进行数值计算.三维光弹性“冻结”切片法用于详细分析两个椭球体的模型,给出几个切面的应力分布,所得结果σ_z与积分方程法相近,并将结果应用于分析不规则岩石力学试件实测资料的整理.     

BASIC EQUATIONS, THEORY AND PRINCIPLE OF COMPUTATIONAL STOCK MARKET (Ⅲ)—BASIC THEORIES

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金融衍生产品的力学方法分析（Ⅰ）——期指价格基本方程

类似连续介质力学方法,将期指价格变化看成是连续、有规律可寻的。根据期指特点,建立期指价格变化的基本方程。这是一个微分方程,其解显示时间与价格呈对数圆形关系。若将时间理解为相应价格的概率,则这一关系与基于统计理论分析的、著名的诺贝尔经济学奖（1997）获得者的期权定价Black-Scholes公式中主要假设-基础资产（在此为期指）价格呈对数正态分布-完全一致。表明了依据完全不同的两种分析方法,也会得到相同的结果。只是Black-Scholes是用假设给出,而作者则从微分方程的解推出。     

SOLUTION OF SIMULTANEOUS EQUATIONS OF COSINE LAW ARISING FROM SUBJECTIVITY GEOMETRY

This paper discusses the solution of a group of two-order six elements rooted algebraicsimultaneous equations set up by cosine law arising from the application example ofsubjectivity geometry.By means of the implicit function theorem,this paper proves thatthere exists a unique real solution of those equations.Transforming this problem into anunconstrained nonlinear optimization problem,the solution can be found by knownmethods.A numerical example by descent method is given.     

Pile Analysis by Simple Integral Equation Methods

Two simple integral equation methods are proposed for the analysisof vertical loaded pile.One of them is:let the axisymmetrical loads formedby 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 pointforce.The other is:in addition to the above fictitious loads,the Mind-lin’s vertical forces are distributed along the axis z in[0,L].The form-er reduces the problem of a vertical loaded pile embedded in a half-spacewith the following boundary conditions.     

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 spaceis studied by the Line-Loaded Integral Equation Method(LLIEM).The problem isreduced to pair of one-dimensional Fredholm integral equations of the first kind due to thedistributions of the fictitious loads“Point Ring Couple(PRC)”and“Point Ring Couple inHalf Space(PRCHS”on the axis of symmetry in the interior and external ranges of theshaft occuied respectively.The direct discrete solution of this integral equations may beunstable,i.e.an ill-posed case occurs.In this paper,such an ill-posed Fredholm integralequation of first kind is replaced by a Fredholm integral equation of the second kind withsmall parameter,which provides a stable solution.This method is simpler and easier tocarry out on a computer than the Tikhonov’s regularization method for ill-posed problems.Numerical examples for conical,cylindrical,conical-cylindrical,and parabolic shafts aregiven.     

复合g—收缩映射不动点定理及其应用

任一几何平均收缩比率小于1（简称g-收缩映射）的由完备的非空度量空间M到M的复合序列映射,复合周期映射有在M中的唯一的不动点,文中给出定理应用于一组非线性微分方程以及扁壳轴对称弯曲的耦合的积分方程的解的存在和唯一性证明的应用例子。     

The Solution of Elastostatic Problems and the Principles of Minimum Potential Energy,Minimum Complementary Work,under Fuzzy Boundary Conditions

A Solution of elastostatic problem is defined on the basis of set theory andextended to the cases with fuzzy boundary conditions.Extension is alsogiven for the principles of minimum potential energy and minimum comple-mentary work with fuzzy boundary conditions.A quasisolution of an elasto-static problem is defined as an approximate solution with boundary conditionsmost close to the original.And the existance of quasisolution of an elasto-static problem can be proved on the basis of certain assumptions and thetheorem of minimum elementary potential energy.     

UNIQUENESS OF SOLUTION OF FIELD POINT OF SINGULAR SOURCE OUTSIDE-REGION-DISTRIBUTION METHOD

IntroductionAmethod,inwhichaproblemissolvedbysingularsource(s)outside-region-distribution(s),wheretheboundaryconditionoftheproblemissatisfied,iscalled"SingularSourceOutside-Region-DistributionMethod"(SSORDM).Usnallynon-singularintegralequationisobtainedbysingularsource(s)outSide-region-distribunonconhnuously.Asanearlyuse,singUlarsourcedistribuhoncanbefoundinthemethodofsource-sinkdistributioninfluidmechanicsasisstatedin[I],however,noproblemwasreducedtoanintegralequationatthattime.Asforsol…