内压载荷作用下薄膜椭球的稳定性分析

耿亚南; 蔡宗熙

doi:10.6052/0459-1879-16-142

内压载荷作用下薄膜椭球的稳定性分析

doi: 10.6052/0459-1879-16-142

耿亚南^,,
蔡宗熙

天津大学机械工程学院力学系, 天津 300354

基金项目: 国家自然科学基金（11372212，11172200）和国家重点基础研究发展计划（973）课题（2013CB035402）资助项目.

详细信息

通讯作者:
耿亚南,博士研究生,主要研究方向:超弹性材料的分岔问题.E-mail:gengyn@tju.edu.cn

中图分类号: O343
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出版历程
- 收稿日期: 2016-05-24
- 修回日期: 2016-06-28
- 刊出日期: 2016-11-18

STABILITY OF A PRESSURIZED ELLIPSOIDAL BALLOON

Geng Yanan^,,
Cai Zongxi

Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300354, China

摘要

摘要: 超弹性橄榄状和南瓜状薄膜椭球在内压载荷作用下存在不同的分岔形式.对橄榄状薄膜椭球来说，细长比大于某一临界值时，在一定内压作用下会发生梨形分岔；小于该临界值时，薄膜椭球的分岔行为与圆管的局部起鼓现象相类似.对南瓜状薄膜椭球，无论圆扁，当内压达到某载荷值时都会发生梨形分岔.本文采用能量判据，分析了在压强控制和质量控制两种加载方式作用下，不同形状的薄膜椭球的均匀解及分岔解的稳定性.通过计算要考察的平衡状态及施加小扰动之后状态的能量差来判断当前状态是否稳定，结果表明，在压强控制下，P-V曲线下降段的均匀解和分岔解均为不稳定解.但在质量控制下，在P-V曲线下降段中只有均匀解出现时，均匀解为稳定解；而在均匀解和分岔解共存的区间内，均匀解为不稳定解，分岔解为稳定解.另外，P-V曲线两个上升段的均匀解则均为稳定解.
- 超弹性 /
- 薄膜椭球 /
- 分岔 /
- 能量判据 /
- 稳定性
Abstract: A pressurized ellipsoidal balloon may bifurcate into different shapes depending on its precise shape. For a rugby-shaped balloon, there exists a threshold ratio of the axes in the Z- and R- directions, above which the balloon tends to bifurcate into a pear shape. Otherwise, the pear shape is impossible and when the balloon is slender enough, it may bulge out locally in a symmetric manner more like a tube. However, for a pumpkin-shaped balloon, bifurcation into a pear shape is always possible. In this paper, by using an energy criterion, we determine the stability properties of the primary and bifurcated solutions under pressure control and volume control,respectively. The total energy of the equilibrium state and its disturbed state are calculated, and the di erence between these two states is used to evaluate the stability of current state. Our analyses indicate that under pressure control, both primary and bifurcated solutions that exist on the descending branch of the pressure versus volume curve are unstable, but under volume control, the bifurcated solution is always stable whenever it appears while the primary solution is only stable when there does not exist any bifurcated solution. However, the primary solutions that exist on the two ascending branches are always stable.
- hyperelasticity /
- ellipsoidal balloon /
- bifurcation /
- energy criterion /
- stability

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参考文献(31)

1 Liao L, Pasternak I. A review of airship structural research and development. Progress in Aerospace Sciences, 2009, 45(4):83-96

2 Cathey Jr HM, Fairbrother DA, Tuttle JW, et al. Qualification of the NASA super pressure balloon. In:Proc. of AIAA Balloon Systems Conference, Texas, 2015

3 Zhao X, Wang Q. Harnessing large deformation and instabilities of soft dielectrics:theory, experiment, and application. Applied Physics Reviews, 2014, 1(2):021304

4 Godaba H, Li J, Wang Y, et al. A soft jellyfish robot driven by a dielectric elastomer actuator. IEEE Robotics and Automation Letters, 2016, 1:624-631

5 Pelrine R, Kornbluh R, Kofod G. High-strain actuator materials based on dielectric elastomers. Advanced Materials, 2000, 12(16):1223-1225 3.0.CO;2-2">

6 Zhao B, Chen W, Hu J, et al. An innovative methodology for measurement of stress distribution of inflatable membrane structures. Measurement Science and Technology, 2015, 27(2):025002

7 Jenkins CH. Progress in astronautics and aeronautics:gossamer spacecraft:membrane and inflatable structures technology for space applications, AIAA, Virginia, 2001

8 Kyriacou SK, Humphrey JD. Influence of size shape and properties on the mechanics of axisymmetric saccular aneurysms. Journal of Biomechanics, 1996, 29(8):1015-1022

9 Haslach HW, Humphrey JD. Dynamics of biological soft tissue and rubber:internally pressurized spherical membranes surrounded by a fluid. International Journal of Non-Linear Mechanics, 2004, 39(3):399-420

10 Humphrey JD, Canham PB. Structure mechanical properties and mechanics of intracranial saccular aneurysms. Journal of Elasticity and the Physical Science of Solids, 2000, 61(1-3):49-81

11 Watton P, Hill N, Heil M. A mathematical model for the growth of the abdominal aortic aneurysm. Biomechanics and Modeling in Mechanobiology, 2004, 3(2):98-113

12 Alhayani A, Rodriguez J, Merodio J. Competition between radial expansion and axial propagation in bulging of inflated cylinders with application to aneurysms propagation in arterial wall tissue. International Journal of Engineering Science, 2014, 85:74-89

13 任九生,袁学刚. 人体动脉瘤生成与破裂的力学分析. 应用数学和力学, 2010, 31(5):561-72(Ren Jiusheng, Yuan Xuegang. Mechanics of the formation and rupture of human aneurysms. Applied Mathematics and Mechanics, 2010, 31(5):561-572(in Chinese))

14 Needleman A. Inflation of spherical rubber balloons. International Journal of Solids and Structures, 1977, 13(5):409-421

15 Haughton DM, Ogden RW. On the incremental equations in nonlinear elasticity-Ⅱ. Bifurcation of pressurized spherical shells. Journal of the Mechanics and Physics of Solids, 1978, 26(2):111-138

16 Fu YB, Xie YX. Stability of pear-shaped configurations bifurcated from a pressurized spherical balloon. Journal of the Mechanics and Physics of Solids, 2014, 68:33-44

17 Chater E, Hutchinson J. On the propagation of bulges and buckles. Journal of Applied Mechanics, 1984, 51(2):269-277

18 Haughton DM, Ogden RW. Bifurcation of inflated circular cylinders of elastic material under axial loading-I. Membrane theory for thin-walled tubes. Journal of the Mathematics and Physics of Solids, 1979, 27:179-212

19 Kyriakides S, Chang YC. The initiation and propagation of a localized instability in an inflated elastic tube. International Journal of Solids and Structures, 1991, 27:1085-1111

20 Fu YB, Pearce SP, Liu KK. Post-bifurcation analysis of a thin-walled hyperelastic tube under inflation. International Journal of Non-Linear Mechanics, 2008, 43(8):697-706

21 任九生,程昌钧. 热超弹性圆筒的不稳定性. 力学学报, 2007, 39(2):283-288(Ren Jiusheng, Cheng Changjun. Instability of incompressible thermo-hyperelastic tubes. Chinese Journal of Theoretical and Applied Mechanics, 2007, 39(2):283-288(in Chinese))

22 Alexander H. Tensile instability of initially spherical balloons. International Journal of Engineering Science, 1971, 9:151-162

23 Liang XD, Cai SQ. Shape bifurcation of a spherical dielectric elastomer balloon under the actions of internal pressure and electric voltage. Journal of Applied Mechanics, 2015, 82(10):101002

24 Chen Y. Stability and bifurcation of finite deformations of elastic cylindrical membranes-Part I. stability analysis. International Journal of Solids and Structures, 1997, 34:1734-1749

25 Fu YB, Xie YX. Stability of localized bulging in inflated membrane tubes under volume control. International Journal of Engineering Science, 2010, 48(11):1242-1252

26 FengWW. Inflation of a viscoelastic ellipsoidal neo-Hookean membrane. AIAA Journal, 1976, 14(5):672-675

27 Sagiv A. Inflation of an axisymmetric membrane:stress analysis. Journal of Applied Mechanics, 1990, 57(3):682-687

28 Geng YN, Huang JX, Fu YB. Shape bifurcation of a pressurized ellipsoidal balloon. International Journal of Engineering Science, 2016, 101:115-125

29 武际可, 苏先樾. 弹性系统的稳定性:科学出版社, 1994(Wu Jike, Su Xianyue. Theory of Elastic Stability. Beijing:Science Press, 1994 (in Chinese))

30 Knops RJ, Wilkes E. Theory of elastic stability. Handbuck der physik, 1973, VI a/3:125-302

31 Ogden RW. Large deformation isotropic elasticity-On the correlation of theory and experiment for incompressible rubberlike solids. Proceedings of the Royal Society of London A:Mathematical, Physical and Engineering Sciences, 1972, 326(1567):565-584

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