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边界为三角形或四边形时反平面弹性或Laplace方程中的退化尺寸问题

陈宜周

陈宜周. 边界为三角形或四边形时反平面弹性或Laplace方程中的退化尺寸问题[J]. 应用数学和力学, 2012, 33(4): 500-512. doi: 10.3879/j.issn.1000-0887.2012.04.010
引用本文: 陈宜周. 边界为三角形或四边形时反平面弹性或Laplace方程中的退化尺寸问题[J]. 应用数学和力学, 2012, 33(4): 500-512. doi: 10.3879/j.issn.1000-0887.2012.04.010
CHEN Yi-zhou. Degenerate Scale Problem in Antiplane Elasticity or Laplace Equation for Contour Shapes of Triangles or Quadrilaterals[J]. Applied Mathematics and Mechanics, 2012, 33(4): 500-512. doi: 10.3879/j.issn.1000-0887.2012.04.010
Citation: CHEN Yi-zhou. Degenerate Scale Problem in Antiplane Elasticity or Laplace Equation for Contour Shapes of Triangles or Quadrilaterals[J]. Applied Mathematics and Mechanics, 2012, 33(4): 500-512. doi: 10.3879/j.issn.1000-0887.2012.04.010

边界为三角形或四边形时反平面弹性或Laplace方程中的退化尺寸问题

doi: 10.3879/j.issn.1000-0887.2012.04.010
详细信息
    通讯作者:

    陈宜周(1933—), 男,浙江余姚人,教授(Tel:+86-511-88780780;E-mail:chens@ujs.edu.cn).

  • 中图分类号: O34;O241.85;174.5

Degenerate Scale Problem in Antiplane Elasticity or Laplace Equation for Contour Shapes of Triangles or Quadrilaterals

  • 摘要: 对于反平面弹性或Laplace方程的外部边值问题, 给出了三角形或四边形周界时一系列退化尺寸问题的解,并利用了Schwarz-Christoffel 保角映象.证实当某一尺寸“R”等于它的临界值或一个单位值时,一个形式上简明的复位函数满足单位圆上位移为0的条件,或w=0.这就意味着在实际平面上的退化尺寸已经得到.最后,退化尺寸可从某些特殊积分得出,这些积分依赖于保角映象中的诸参数.给出了三角形或四边形周界时一系列退化尺寸问题的数值结果.
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出版历程
  • 收稿日期:  2011-11-24
  • 修回日期:  2012-01-20
  • 刊出日期:  2012-04-15

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