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

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Using Generalized Variational Principles to Resolve the St. Venant’s Torsional Bar with a Crack

摘要: 本文根据钱伟长教授的弹性力学小位移非协调元的广义变分原理^[1]采用裂纹尖端奇异元素^[2]及本文作者给出的八节点等参数环绕元素,对含有径向纵裂纹的圣维南扭转问题进行了有限元分析,并与参考文献[2]的计算结果进行了比较,计算结果表明,用本文提供的方法,在自由度很低的情况下,就可得到相当满意的收敛解答.

Abstract: According to generalized variational principles suitable for linear elastic incompatible displacement elements given by Professor Chien Wei-zang, using crack tip singular element and isoparametric surrounding element given by the author of this paper, we will study the St. Venant's torsional bar with a radial vertical crack and compare the present computed results with the results of reference [2], The present computed results show that, using the method provided in this paper, satisfactory convergent solution can be obtained under lower degree of freedom.

[1]	钱伟长,《广义变分原理》,知识出版社(1985).
[2]	蔡承文等,计算St. Venant扭转时K_Ⅱ的任意高阶奇应变单元,固体力学学报,1 (1983).