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

作　　者：陈宜周 

机构地区：[1]Division of Engineering Mechanics,Jiangsu University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2012年第4期525-538,共14页应用数学和力学（英文版）

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 partic- ular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.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 partic- ular integrals depending on certain parameters in the mapping function. The numerical results of degenerate sizes for the shapes of triangles or quadrilaterals are provided.

关 键 词：degenerate scale conformal mapping technique shape of triangle or quadri-lateral antiplane elasticity 

分 类 号：O175.8[理学—数学]