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中文核心期刊

热超弹性圆筒的不稳定性

Instability of incompressible thermo-hyperelastic tubes

  • 摘要: 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.

     

    Abstract: Instability of non-uniform deformations of an incompressiblethermo-hyperelastic tube, subjected to internal pressure and axial stretch,is examined within the framework of finite elasticity. When the inflationpressure is small, a thin-walled tube undergoes a uniform inflation. Butwhen the inflation pressure is larger than a certain critical value, thethin-walled tube undergoes a strikingly non-uniform deformation. One partbecomes highly distended as a bubble while the rest remains lightlyinflated. But a thick-walled tube always undergoes a uniform inflationeven if the pressure attains a very high value. A critical thickness for thetube to have an instability deformation is given based on the deformation curves along with its slope. Furthermore, theeffect of axial stretch and temperature on the deformation is discussed.

     

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