球形扁壳在冲击载荷作用下的超临界变形

SUPERCRITICAL DEFORMATIONS OF SHALLOW SPHERICAL SHELLS UNDER IMPACT

本文利用Pogorelov提出的薄亮稳定性几何学理论,研究了球形扁壳在冲击作用下的超临界变形行为。这种方法是建立在实验观察中,壳结构的大变形是以近似于一种等距变换的方式产生的。首先,给出了壳体变形能的近似表达式,在此基础上,考虑了两种不同的在扁球壳顶部的冲击方式,利用能量原理,得到了描述运动的控制方程。从而给出扁球壳中心最大凹陷半径随冲击载荷变化的近似表达式,并将此结果与实验进行了比较,二者吻合的还是比较好的。

This paper discusses the supercritical deformation of shallow spherical shells under impact by using the geometrical theory of thin-shell stability proposed by A. V. Pogorelov. This method is based on the experimental observations,that the large deformation of shell takes a form resembling one of the forms of its isometric transformation. First of all,the approximate formulae of deformation energy of shell are derived. Secondly, two different ways of impact on apex of shallow spherical shell are considered and the governing equation is derived by using the energy balance. Finally, an approximate formulae of maximal hollow radius depending on impact velocities are derived. The present analysis is shown to agree with some available experimental results.