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本文利用弹性力学三维问题的Kelvin解,推导了无限均匀弹性体中园扭矩产生的应力和位移,建立了回转体扭转问题的边界积分方程式,并编制了计算程序,用计算机计算了内含回转椭球形空洞或具有不同剪切模量的回转椭球体的园柱受纯扭时的应力集中系数,根据计算分析结果,对应力集中系数的规律进行了探讨。计算结果在内含物剪切模量为零时与诺埃伯的近夹解吻合。本文得出的结果可供园柱构件抗扭强度计算参考。
In this paper, the Kelvin solution to the three-dimensional problem of elasticity is used to derive the stresses and displacements generated by the torsion of an infinitely uniform elastic body. A boundary integral equation for the torsion of a revolving body is established and a calculation program is developed. The stress concentration factor of pure hollow torsion of spherical hollows or ellipsoids with different shear moduli is discussed. According to the calculation and analysis results, the law of stress concentration factor is discussed. The calculated results are in agreement with the near-clamping of Noelberg when the shear modulus of the inclusion is zero. The results obtained in this paper can be used to calculate the torsional strength of cylindrical columns.