含多个椭圆孔或裂纹的圆柱体扭转问题  

TORSION OF CIRCULAR SHAFT CONTAINING MULTIPLE ELLIPTICAL HOLES OR CRACKS

作　　者：黄成[1] 高存法[1] 

机构地区：[1]南京航空航天大学航空宇航学院,南京210016

出　　处：《工程力学》2011年第4期28-34,共7页Engineering Mechanics

基　　金：国家自然科学基金项目(10672076)

摘　　要：基于复势函数理论,提出了一种既简洁又直观的方法来研究含多个椭圆孔或裂纹的圆柱体的Saint-Venant扭转问题。首先,应用保角变换技术以及Faber级数和Fourier级数展开方法,给出了孔边应力和抗扭刚度的半解析解;然后,当椭圆退化成裂纹时推导了裂纹尖端的应力强度因子解。最后,通过几组数值算例,讨论了各种参数的变化对孔周应力集中、抗扭刚度以及应力强度因子的影响,并就特殊情况与文献中的一些结果进行了比较,结果表明了该方法具有精度高,收敛速度快等优点。A straightforward and concise approach is proposed to analyze the Saint-Venant＇s torsion of a circular shaft containing multiple holes or cracks based on a complex variable method.The semi-analytic solutions for shear stresses and torsional rigidity are first given by introducing the Faber series expansion,Fourier series expansion and conformal mappings.Then,when the elliptical holes degenerate into cracks,the expression for the stress intensity factors of cracks is also derived.Finally,the effects of the parameters on the holes stress concentration,torsional rigidity and the stress intensity factors are studied through several numerical examples.It is shown from the obtained results for special examples that the method presented in this paper has many advantages such as high accuracy and good convergence.

关 键 词：Saint-Venant扭转 复变函数 Faber级数 抗扭刚度 应力强度因子 

分 类 号：O343.4[理学—固体力学]