受内压热超弹性球壳的不稳定性

Instability of Inflated Incompressible Thermo-hyperelastic Spherical Shells

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.

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.