Plane-stress analysis of a holed membrane at finite equibiaxial stretch

IF 1.7 4区 工程技术 Q3 MATERIALS SCIENCE, MULTIDISCIPLINARY
Idan Z Friedberg, Gal deBotton
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引用次数: 0

Abstract

An equibiaxially stretched thin neo-Hookean circular membrane with a hole at its center under plane-stress condition is analyzed within the framework of finite deformation elasticity. Initially, we introduce a novel form for the differential governing equation to the problem. This enables the introduction of a closed-form solution in the limit of infinite stretch. Comparison of this solution to corresponding finite element simulations reveals a neat agreement for stretch ratios larger than 2.5. In the practically important case of a small hole, at the circumference of the hole, the stress concentration factor is 4 and the tangential stretch ratio is twice the applied far-field stretch ratio. These values are double the corresponding ratios in the well-known limit of infinitesimal deformation.
有限等轴拉伸时孔膜的平面应力分析
我们在有限变形弹性框架内分析了在平面应力条件下等轴向拉伸的中心有孔的新胡克圆形薄膜。首先,我们为该问题引入了一种新的微分控制方程形式。这样就能在无限拉伸极限引入闭式解。将该解法与相应的有限元模拟进行比较,发现在拉伸比大于 2.5 时,两者的解法完全一致。在一个小孔的重要实际情况中,在孔的圆周处,应力集中系数为 4,切向拉伸比是应用远场拉伸比的两倍。这些数值是众所周知的无限小变形极限下相应比率的两倍。
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来源期刊
Mathematics and Mechanics of Solids
Mathematics and Mechanics of Solids 工程技术-材料科学:综合
CiteScore
4.80
自引率
19.20%
发文量
159
审稿时长
1 months
期刊介绍: Mathematics and Mechanics of Solids is an international peer-reviewed journal that publishes the highest quality original innovative research in solid mechanics and materials science. The central aim of MMS is to publish original, well-written and self-contained research that elucidates the mechanical behaviour of solids with particular emphasis on mathematical principles. This journal is a member of the Committee on Publication Ethics (COPE).
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