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Structural Engineering and Mechanics Volume 64, Number 6, December25 2017 , pages 695-701 DOI: https://doi.org/10.12989/sem.2017.64.6.695 |
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Some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation |
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Y.Z. Chen
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| Abstract | ||
| This paper investigates some general properties in the degenerate scale problem of antiplane elasticity or Laplace equation. For a given configuration, the degenerate scale problem is solved by using conformal mapping technique, or by using the null field BIE (boundary integral equation) numerically. After solving the problem, we can define and evaluate the degenerate area which is defined by the area enclosed by the contour in the degenerate configuration. It is found that the degenerate area is an important parameter in the problem. After using the conformal mapping, the degenerate area can be easily evaluated. The degenerate area for many configurations, from triangle, quadrilles and N-gon configuration are evaluated numerically. Most properties studied can only be found by numerical computation. The investigated properties provide a deeper understanding for the degenerate scale problem. | ||
| Key Words | ||
| degenerate scale problem; degenerate area; maximum property for degenerate area; laplace equation; conformal mapping | ||
| Address | ||
| Y.Z. Chen : Division of Engineering Mechanics, Jiangsu University, Zhenjiang, Jiangsu, 212013 P.R. China | ||