带裂纹方形截面杆扭转问题的自然边界元与有限元耦合法

根据基于区域分解的自然边界元与有限元的耦合法,研究了带裂纹的方形截面杆的扭转问题,编制了耦合法计算程序,计算了几种尺寸截面的抗扭刚度、截面各点的应力及裂纹的应力强度因子,并绘出了裂纹尖端的应力分布图.计算中,还探索了松弛因子对迭代收敛速度的影响.从实践上证实了自然边界元与有限元的耦合法所具有的优点.     

圆内平面弹性问题的边界积分公式

根据双解析函数可以得到单位圆内平面弹性问题应力函数的边界积分公式,但式中包含强奇异积分,不能用于直接计算．将边界上的应力函数展开为Fourier级数,再利用广义函数论中的几个公式进行卷积计算,可以得到不含强奇异积分核的边界积分公式,通过边界的应力函数值和法向导数的积分,直接得到圆内应力函数值,并给出几个算例,表明该结果用于求解单位圆内平面弹性问题十分方便．     

Numerical residual elimination method of finite differential equations

In this paper,a new elimination of finite differential equations has been discussed.It applies the numerical direct iteration to obtain the residual equations,in which the number of unknowns has been reduced greatly.The solution process is simple and efficient,and the solution is exact     

BOUNDARY INTEGRAL FORMULAS FOR ELASTIC PLANE PROBLEM OF EXTERIOR CIRCULAR DOMAIN

After the stress function and the normal derivative on the boundary for the plane problem of exterior circular domain are expanded into Laurent series, comparing them with the Laurent series of the complex stress function and making use of some formulas in Fourier series and the convolutions, the boundary integral formula of the stress function is derived further. Then the stress function can be obtained directly by the integration of the stress function and its normal derivative on the boundary. Some examples are given. It shows that the boundary integral formula of the stress function is convenient to be used for solving the elastic plane problem of exterior circular domain.     

BOUNDARY INTEGRAL FORMULA OF ELASTIC PROBLEMS IN CIRCLE PLANE

IntroductionConcerningtheelasticplaneprobleminaunitcircle ,ZhengShenzhouandZhengXueliangdevelopedaboundaryintegralformulaofthestressfunction[1]:Φ(r,θ) =-( 1 -r2 ) 24π ∫2π0ν( φ)1 -2rcos(θ-φ) r2 dφ　　 12π∫2π011 -2rcos(θ-ω) r2 dω∫2π0μ( φ)1 -cos(ω-φ) dφ　　 1 -r22π∫2π0μ( φ)1 -2rcos(θ -φ) r2 dφ　　 ( 0 ≤r <1 ) ,( 1 )whereμ(θ) =Φ(r,θ) ｜r=1,ν(θ) = Φ n r=1= Φ r r=1.Intheformula ( 1 )theseconditemisastrongsingularintegral,itshouldbeunderstoodasanintegra…     

差分方程解的数值余量消元法

本文提出一种新的消元方法,该法利用数值的直接迭代产生余量方程,从而构成已消去很多未知量的线性方程组.本文的方法具有求解简便、精确和快速的优点.