1) hypersingular integral equation method
超奇异积分方程方法
1.
Starting rigorously from the three-dimensional theory of transversely isotropic elasticity, this paper presents exactly solutions of displacement jumps, singular stress fields and stress intensities factor near the front edge of mode I penny-shaped crack in transversely isotropic materials with the use of hypersingular integral equation method.
严格从三维横观各向同性弹性理论出发,使用超奇异积分方程方法,精确地求得了I型圆形片状裂纹前沿的位移间断、奇性应力场和应力强度因子。
2) super-singular integral equation method
超奇异积分方程法
3) hypersingular integral equation
超奇异积分方程
1.
Using Somigiliana's formula, the general solutions and hypersingular integral equations for a three-dimensional impermeable crack problem in an infinite transversely isotropic piezoelectric solid under mechanical and electrical loads are given.
采用Somigiliana公式给出了三维横观各向同性压电材料中的非渗漏裂纹问题的一般解和超奇异积分方程,其中未知函数为裂纹面上的位移间断和电势间断。
2.
As the cracks lie in one side of the bimaterial plane,the problem is reduced with finite-part integral conceptions to a set of hypersingular integral equations,in which the unknown functions are the displacement discontinuities on the crack surfaces.
基于双材料平面问题的弹性力学基本解,使用边界积分方程方法,在有限部积分的意义下,将双材料平面单侧多裂纹问题归结为1组以裂纹面位移间断为未知函数的超奇异积分方程组,根据有限部积分原理为其建立了数值算法,并给出了相应的应力强度因子计算公式。
3.
In this paper, the problem of an arbitrarily shaped planar crack which is perpendicular to the interface of bimaterial and loaded by interior normal pressure is studied by means of the method of hypersingular integral equation in three dimensional fracture mechanics.
利用三维断裂力学的超奇异积分方程方法,对双材料空间中重直于界面的平片裂纹Ⅰ型问题进行了研究。
4) Hyper-singular integral equation
超奇异积分方程
1.
To simplify the calculations of wheel-rail contact force and governing equations,a surface crack problem in a semi-infinite space was reduced to solving a set of hyper-singular integral equations with displacement jumps as unknown functions.
为简化轮轨接触力和控制方程的计算,利用Hadamard有限部积分的概念,将半空间表面裂纹问题归化为求解一组以位移间断作为未知函数的超奇异积分方程;采用边界元法离散该积分方程组,并对方程组中出现的超奇异积分提出了特殊的数值处理方法。
2.
A radial crack in an elastic plane with a circular inclusion is investigated by use of a hyper-singular integral equation method.
根据含圆形嵌体平面问题在极坐标下的弹性力学基本解,使用Betti互换定理,在有限部积分意义下将问题归结为两个以裂纹岸位移间断为基本未知量、对于Ⅰ型和Ⅱ型问题相互独立的超奇异积分方程,对含圆形嵌体弹性平面中的径向裂纹问题进行了研究。
3.
Based on the fundamental solution of the elastic mechanics on the half-plane body with free boundary,and using Bitt s low, the stress-displacement relation, Hooke s low, and the stress boundary condition of the crack, the hyper-singular integral equations to describe this problem was \{derived\}; through suitable integral transforms, we established the correspondi.
对固定边半平面含平行于边界裂纹的问题进行研究,由固定边半平面弹性体的弹性力学基本解,利用换功定律、位移-应变关系、胡克定律及裂纹岸应力边界条件,得到描述该问题的超奇异积分方程组,并通过适当的积分变换,在有限部积分的意义下建立了相应的数值方法。
5) hypersingular integral equations
超奇异积分方程
1.
Then,this crack problem is reduced to solving a set of hypersingular integral equations coupled with boundary integral equations.
应用位移基本解,磁电热弹材料三维裂纹问题被转化为求解一组以裂纹表面位移间断为未知函数的超奇异积分方程问题。
2.
Using Kelvin s solutions and the concepts of finite-part integral,a set of hypersingular integral equations to solve the inclusion problems in two dimension elasticity is derived,and its numerical method is then proposed by combining the finite-part integral method with the boundary element method.
利用Ｋｅｌｖｉｎ解及有限部积分的概念和方法，导出求解含夹杂二维有限弹性体的超奇异积分方程，继而使用有限部积分与边界元结合的方法，为其建立了数值求解方法，即有限部积分与边界元法。
3.
Using the concepts and method of finite-part integrals, the hypersingular integral equations of a plane crack loaded by arbitrary loads is proved exactly.
本文利用有限部积分的概念和方法,严格地证明了三维弹性体中受任意载荷作用的平片裂纹问题的超奇异积分方程组,并对未知解的性态作了理论分析,得到了性态指数,在此基础上通过主部分析,精确地求得了裂纹前沿光滑点附近的奇性应力场,从而找到了以裂纹面位移间断(位错)表示的应力强度因子表达式,最后对所得的超奇异积分方程组建立了数值法,并用此计算了若干典型的平片裂纹问题,数值结果令人满意。
6) singular integral equation method
奇异积分方程法
补充资料：Jackson奇异积分
Jackson奇异积分
Jackson singular integral
血c地阅奇异积分【J扭d，扣应粤血r血l魄口l;及耀袱oaaeo.r”，p”诫“”Te印即」，Jacl侣on算子(」ackson openl-tor) 形如 +派 u(f.、卜上ff(二+。)K.(。)、。 兀J的积分，其中表达式凡(·，一丽资不}晋揣导」‘，一，，，，~·称为J故此on核(Jacl侣onkemel).D.Jacl侣on(汇11)在通过函数f的连续模。(f，1/n)或者f的k)1阶导数的连续模来估计f的最佳逼近时首先使用了这种积分.1朗kson奇异积分是一个正算子，并且是2”一2阶的三角多项式;它的核K。(u)可以表示为下列形式:戈(幻=A+p{”一2邸:十…十p;几二;邸(2。一2)t，其中注=z/2，而p子“一之=1一3/(Zn，)，刀=1，2，·…估计式 .。.(f，;)一，(、)、、6。卜，粤1成立.一一
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条