一组适合于带纵向裂纹柱体圣维南扭转的等参数元素
A Group of Isoparametric Elements Suitable for St.Venant's Torsion of a Bar with Cracks
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摘要: 本文给出一组新的适合于带纵向裂纹柱体圣维南扭转的等参数元素,它们分别是八结点等参数元素、在裂纹尖端具有r-1/2奇异性的“1/4”八结点等参数元素及八结点过渡元素.利用这些元素,对含有径向纵裂纹的圆柱体进行了圣维南扭转计算.计算结果表明,本文给出的等参数元素有较高的精度、较好的收敛性及快的收敛速度,同时还具有程序简单、省机时等优点,所以特别适合于实际的工程计算.Abstract: In this paper,we shall give a group of new isoparametric elements suitable.for St.Wenant's torsion of a bar with vertical cracks.These elements are eight-point isoparametric element,quarter eight-Point isoparametric element and eight-point isoparametric transition element.Among these elements,the second and the third elements possess the singularity of order r-1/2 at crack tip.Using these elements,wehave completed the calculations of St.Venant's torsion for a cylinder with a radial vertical crack.The calculated results show that the isoparametric elements given bythis paper have ideal accuracy,good convergence.high speed of convergence,low freedom and little computational time,and so they can be widely applied to practice.
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Key words:
- singular finite element /
- transition finite element /
- fractur emechanics /
- St
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[1] 蔡承文等,计算St.Venant扭转时KⅡ的任意高阶奇应变单元,固体力学学报(1983),92-99. [2] 钱伟长,《广义变分原理》,知识出版社(1985). [3] 范秀昌,用位移非协调广义变分原理解含裂纹体的圣维南扭转问题,应用数学和力学,10,(2)(1989),189-196. [4] R.S.Barsoum,Triangular quarter-point elements as elastic and perfectly-plastic crack tip elements,Int.J.Num.Mech.Engng.,11(1977),85-97. [5] C.Manu,Quadratic isdparametric elements as transition element,Engneg.Frach.Mech.,24,4(1986),509-512. -
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