翻转的Varga材料球壳的渐近分支

摘要

It is well-known that a spherical shell may not stay spherical after eversion and it may prefer to adopt a wrinkled configuration. In this case, a bifurcation solution occur. In this paper, WKB method was used to analyse the buckling of an everted Varga spherical shell of incompressible, isotropic hyper-elastic material. For AB=O(1) a simple asymptotic expression is obtained for the critical ratio of the inner radius to the outer radius with the mode number large enough. The analytical results perfectly coincide with the numerical results over almost the whole mode-number regin.%众所周知,弹性球壳在翻转后可能不再保持球壳形状而出现起皱现象,也就是出现分支解.本文运用WKB方法,分析了各向同性且不可压缩的超弹性Varga材料球壳翻转后的变形问题.在大模数情形下,对于A-B=O(1),得到了球壳内、外径比的分支临界值的渐近表达式.对模数区域内几乎所有的模数,分析结果与数值结果吻合得很好.