热超弹性圆筒的不稳定性

应用有限变形弹性理论分析了受内压和轴向拉伸作用的不可压热超弹性圆筒发生非均 匀变形的不稳定性问题. 受内压和轴向拉力作用的薄壁圆筒，当内压较小时，圆筒发生稳定 的均匀膨胀变形；当内压大于某一临界值时，圆筒产生复杂的非均匀变形，其一部分膨胀变 形很大，形如``灯泡'状，而另一部分仅仅是轻微膨胀，且此时的变形是不稳定的. 但对厚 壁圆筒而言，不论压力如何，总是发生稳定的均匀膨胀变形. 根据圆筒的变形曲线，给出了 圆筒可以发生不稳定变形的临界厚度. 同时，讨论了轴向拉伸和温度场对圆筒变形的影响.

INSTABILITY OF INCOMPRESSIBLE THERMO-HYPERELASTIC TUBES

Instability of non-uniform deformations of an incompressible thermo-hyperelastic tube, subjected to internal pressure and axial stretch, is examined within the framework of finite elasticity. When the inflation pressure is small, a thin-walled tube undergoes a uniform inflation. But when the inflation pressure is larger than a certain critical value, the thin-walled tube undergoes a strikingly non-uniform deformation. One part becomes highly distended as a bubble while the rest remains lightly inflated. But a thick-walled tube always undergoes a uniform inflation even if the pressure attains a very high value. A critical thickness for the tube to have an instability deformation is given based on the deformation curves along with its slope. Furthermore, the effect of axial stretch and temperature on the deformation is discussed.