受内压热超弹性球壳的不稳定性

上海大学学报(自然科学版) ›› 2007, Vol. 13 ›› Issue (6): 732-735 .

受内压热超弹性球壳的不稳定性

任九生1，2，程昌钧1，2

1.上海大学理学院，上海 200444；
2.上海大学上海市应用数学和力学研究所，上海 200072

收稿日期:2006-09-08 修回日期:1900-01-01 出版日期:2007-12-20 发布日期:2007-12-20
通讯作者: 任九生1，2

Instability of Inflated Incompressible Thermohyperelastic Spherical Shells

REN Jiu-sheng1,2,CHENG Chang-jun1,2

1. School of Sciences, Shanghai University, Shanghai 200444, China;
2. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, China

Received:2006-09-08 Revised:1900-01-01 Online:2007-12-20 Published:2007-12-20
Contact: REN Jiu-sheng1,2

摘要/Abstract

摘要：

应用有限变形弹性理论分析了受内压作用的不可压热超弹性球壳发生非对称变形的不稳定性问题.当内压较小时，薄壁球壳发生对称的均匀膨胀变形；当内压大于某一临界值时，产生复杂的非对称变形，其一部分膨胀变形很大，而另一部分仅仅是轻微膨胀，且其形状逐渐远离球形，且此时的变形是不稳定的.厚壁球壳总是发生稳定的均匀膨胀变形.根据球壳的变形曲线，给出了球壳发生不稳定变形的临界厚度.同时，讨论了温度场对球壳变形的影响.

关键词: 不可压热超弹性材料, 不稳定性, 非对称变形, 临界厚度, 温度的影响

Abstract:

Instability of asymmetric deformations of an incompressible thermo-hyperelastic spherical shell, subjected to internal pressure, is examined within the framework of finite elasticity. When the inflation pressure is small, the thin-walled shell undergoes a symmetric inflation. But when the inflation pressure is larger than a certain critical value, the thin-walled shell undergoes an asymmetric deformation. One part becomes highly distended while the rest remains lightly inflated and the shell takes up an aspherical shape. But the thick-walled shell always undergoes a symmetric inflation even if the pressure reaches a very high value. A critical thickness for the shell to take an instability deformation is given based on the change regulation of the deformation curves along with its slope. Furthermore, the effect of temperature on the deformation is discussed.

Key words: asymmetric deformation, critical thickness

, effect of temperature, instability,

incompressible thermo-hyperelastic material

任九生;程昌钧;. 受内压热超弹性球壳的不稳定性[J]. 上海大学学报(自然科学版), 2007, 13(6): 732-735 .

REN Jiu-sheng;CHENG Chang-jun;. Instability of Inflated Incompressible Thermohyperelastic Spherical Shells[J]. Journal of Shanghai University（Natural Science Edition）, 2007, 13(6): 732-735 .