A Rational Derivation of a Tube Law from Shell Theory
A Rational Derivation of a Tube Law from Shell Theory
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DOI：
10.1093/qjmam/hbq020
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发表时间：
2010-11-01
影响因子：
0.9
通讯作者：
Waters, Sarah L.
中科院分区：
文献类型：
--
作者：
Whittaker, Robert J.;Heil, Matthias;Waters, Sarah L.
本文研究具有轴向均匀椭圆截面的薄壁弹性长管的小振幅变形。管受到轴向预应力，并且变形由施加的跨壁压力引起。近似管法（连接跨壁压与横截面积及其轴向导数）是从壳理论中的杰出的渐近极限，其中管的行为是由恢复力从轴向预应力和方位角弯曲为主。这是可能的，因为由跨壁压力和轴向力两者引起的管的变形可以通过轴向变化幅度的单个方位角变形模式描述为非常好的近似。将所得管法与全壳方程的数值解进行了比较，发现吻合良好（只要管足够长，壁不太薄，面内剪切可以忽略不计）。我们讨论了应用我们的研究结果的可折叠管流动的建模。
We consider small-amplitude deformations of a long thin-walled elastic tube having an initially axially uniform elliptical cross section. The tube is subject to an axial pre-stress, and the deformations result from an applied transmural pressure. An approximate tube law (linking the transmural pressure with the cross-sectional area and its axial derivatives) is derived from shell theory in the distinguished asymptotic limit in which the tube's behaviour is dominated by the restoring forces from the axial pre-stress and azimuthal bending. This is possible because the deformations of the tube induced by both the transmural pressure and the axial forces can be described, to very good approximation, by a single azimuthal mode of deformation of axially varying amplitude. The resulting tube law is compared with numerical solutions of the full shell equations and good agreement is found (provided the tube is sufficiently long and the wall not too thin so that in-plane shearing is negligible). We discuss the applications of our results to the modelling of flow in collapsible tubes.