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丁皓江, 彭南陵, 李育. 受r~n分布载荷的楔:佯谬的解决[J]. 力学学报, 1997, 29(1): 62-73. DOI: 10.6052/0459-1879-1997-1-1995-197
引用本文: 丁皓江, 彭南陵, 李育. 受r~n分布载荷的楔:佯谬的解决[J]. 力学学报, 1997, 29(1): 62-73. DOI: 10.6052/0459-1879-1997-1-1995-197
THE WEDGE SUBJECTED TO TRACTIONS IN PROPORTION TO r n : A PARADOX OX RESOLVED[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(1): 62-73. DOI: 10.6052/0459-1879-1997-1-1995-197
Citation: THE WEDGE SUBJECTED TO TRACTIONS IN PROPORTION TO r n : A PARADOX OX RESOLVED[J]. Chinese Journal of Theoretical and Applied Mechanics, 1997, 29(1): 62-73. DOI: 10.6052/0459-1879-1997-1-1995-197

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

  • 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,对此本文也予以解决

     

    Abstract: 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...

     

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