受r^n分布载荷的楔:佯谬的解决  

THE WEDGE SUBJECTED TO TRACTIONS IN PROPORTION TO r n : A PARADOX OX RESOLVED

作　　者：丁皓江[1] 彭南陵[2] 李育 

机构地区：[1]浙江大学土木系 [2]南昌大学工程力学研究所 [3]Boston大学

出　　处：《力学学报》1997年第1期62-73,共12页Chinese Journal of Theoretical and Applied Mechanics

摘　　要：对表面受与ｒｎ（ｎ≥０）成正比的分布载荷的楔，当楔顶角２α与ｎ之间满足一定关系时，经典解为无穷大，这是一个佯谬．本文采用复变函数方法，研究了这个佯谬的所有情形，并发现存在二次佯谬，即对某些特定的（ｎ，α），佯谬解仍为无穷大。The classical solution for the stress distribution in an elastic wedge subjeted to tractions in proportion to r n(n0) becomes infinite when the wedge angle 2α and n satisfy certain relations. This paradox has been resolved by Demsey and Ting when n=0 ,and when n>0 and 2α=π or 2π it has been resolved by Wang Minzhong,however,the researches above provide only a few parts of the resolution for the paradox. In this paper we study all the cases of this paradox by adopting the method of complex functions.We obtain a solution to the paradox and discover that it is still infinite for some special values of (n,α) ,this second paradox has also been resolved in the paper.

关 键 词：楔体 佯谬 弹性力学 

分 类 号：O343[理学—固体力学]