半无限弹性体表面在轴对称扭转荷载作用下的弹性力学问题  

The Problem of Elasticity for a Semi-Infinite Solid Under the Action of the Axisymmetric Torsional Loads on its Surface

作　　者：王凯[1] 

机构地区：[1]东南大学交通学院,南京210096

出　　处：《力学季刊》2012年第3期420-426,共7页Chinese Quarterly of Mechanics

摘　　要：本文首先采用位移函数法和汉克尔变换公式推导了表面受轴对称扭转荷载作用的半无限弹性体内应力与位移分量的通用表达式。在此基础上进一步推导了表面在轴对称扭转剪应力作用下半无限弹性体内应力与位移分量的表达式,纠正了日本著名学者牟岐鹿楼早先推导的该表达式中的一些错误。文章最后推导了表面在轴对称扭矩作用下半无限弹性体内应力与位移分量的表达式,由于该表达式满足弹性力学的所有方程和边界条件,因而是该问题的真正解答。The general expressions for the stress and the displacement components in a semi-infinite solid subjected to axisymmetric torsional loads on its surface are firstly derived by the displacement function method and the formula of the Hankel transform. The expressions for the stress and the displacement components in a semi-infinite solid under the action of the axisymmetric torsional shear stresses were fur- ther derived and some errors in the expressions which were derived by famous scholar Muki of Japan pre- viously were redressed. And finally, the expressions for the stress and the displacement components in a semi-infinite solid subjected to an axisymmetric torque on its surface are derived. Because the expressions satisfy all the equations of elasticity and the boundary conditions, they represent the true solution of the problem.

关 键 词：弹性力学问题 半无限弹性体 轴对称扭矩 轴对称弹性体 轴对称扭转荷载 

分 类 号：O34[理学—固体力学] O343[理学—力学]