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

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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.

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Authors and Affiliations

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

    Yi-zhou Chen  (陈宜周)

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  1. Yi-zhou Chen  (陈宜周)
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Correspondence to Yi-zhou Chen  (陈宜周).

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Chen, Yz. Degenerate scale problem in antiplane elasticity or Laplace equation for contour shapes of triangles or quadrilaterals. Appl. Math. Mech.-Engl. Ed. 33, 525–538 (2012). https://doi.org/10.1007/s10483-012-1568-9

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  • DOI: https://doi.org/10.1007/s10483-012-1568-9

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Chinese Library Classification

2010 Mathematics Subject Classification

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