Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure
Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure
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DOI：
10.1103/physreve.99.022803
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发表时间：
2019-02-26
影响因子：
2.4
通讯作者：
Kierfeld, Jan
中科院分区：
文献类型：
--
作者：
Baumgarten, Lorenz;Kierfeld, Jan
我们研究了完整球壳在均布压力p作用下对附加点力的轴对称响应。对于低于经典临界屈曲压力p(C)的压力p，点力压痕不会导致自发屈曲，但势垒必须被克服。能垒最大值处的态代表不稳定驻点的亚临界分支，这些不稳定驻点是到跃迁屈曲状态的过渡态。从非线性扁壳理论出发，得到了能垒高度的封闭解析表达式，便于用延拓技术对其作为压力函数进行有效的数值计算。我们发现两个制度之间有明显的交叉：对于p/p(C)，
We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure p to an additional point force. For a pressure p below the classical critical buckling pressure p(c), indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome. The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state. Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques. We find a clear crossover between two regimes: For p/p(c),