Solution of an orthotropic elliptic plate with an elliptic hole or crack

Hai-Bing Yang, M. Dai, C. Gao
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Abstract

Based on the complex variable method, the problem of an elliptic plate with an elliptic hole or a crack is addressed under uniform tension or pressure imposed on the boundary of the hole and on the edge of the plate. A series solution for the stress field inside the plate is derived using conformal mapping techniques, Faber series and Fourier expansion method. The stress fields around the hole or crack relative to the distance between the hole or crack and the edge of the plate are discussed in several examples. It is found that the hoop stress around the hole and the stress intensity factors at the crack tips increase steeply with deceasing distance between the hole or crack and the edge of the plate.
带椭圆孔或裂纹的正交各向异性椭圆板的解
基于复变方法,研究了椭圆板在椭圆孔边界和椭圆板边缘施加均匀拉力或压力的情况下,带椭圆孔或裂纹的椭圆板问题。利用保角映射技术、Faber级数和傅立叶展开法,导出了板内应力场的级数解。通过几个实例讨论了孔或裂纹周围的应力场与孔或裂纹与板边缘之间距离的关系。结果表明,随着孔或裂纹与板边距离的减小,孔周围的环向应力和裂纹尖端的应力强度因子急剧增大。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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