Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

doi:10.1007/s10483-012-1568-9

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (4): 525-538.doi: https://doi.org/10.1007/s10483-012-1568-9

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Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

陈宜周

Division of Engineering Mechanics, Jiangsu University, Zhenjiang 212013, Jiangsu Province, P. R. China

收稿日期:2011-11-24 修回日期:2011-01-20 出版日期:2012-04-15 发布日期:2012-04-15
通讯作者: Yi-zhou CHEN, Professor, Ph. D., E-mail:chens@ujs.edu.cn E-mail:chens@ujs.edu.cn

Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

Yi-zhou CHEN

Division of Engineering Mechanics, Jiangsu University, Zhenjiang 212013, Jiangsu Province, P. R. China

Received:2011-11-24 Revised:2011-01-20 Online:2012-04-15 Published:2012-04-15
Contact: Yi-zhou CHEN, Professor, Ph. D., E-mail:chens@ujs.edu.cn E-mail:chens@ujs.edu.cn

摘要/Abstract

摘要： This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem (BVP) of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition (or w=0) along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the particular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

Abstract: This paper provides several solutions to the degenerate scale for the shapes of triangles or quadrilaterals in an exterior boundary value problem (BVP) of the antiplane elasticity or the Laplace equation. The Schwarz-Christoffel mapping is used throughout. It is found that a complex potential with a simple form in the mapping plane satisfies the vanishing displacement condition (or w=0) along the boundary of the unit circle when the dimension R reaches its critical value 1. This means that the degenerate size in the physical plane is also achieved. The degenerate scales can be evaluated from the particular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

中图分类号:

陈宜周. Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 525-538.

Yi-zhou CHEN. Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 525-538.

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Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals

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