Holmes Douglas P, Lee Jeong-Ho, Park Harold S, Pezzulla Matteo
Department of Mechanical Engineering, Boston University, Boston, Massachusetts 02215, USA.
Institute of Mechanical Engineering, École Polytechnique Fédérale de Lausanne, Lausanne CH-1015, Switzerland.
Phys Rev E. 2020 Aug;102(2-1):023003. doi: 10.1103/PhysRevE.102.023003.
In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prevalent in a wide range of natural and engineered systems, and may occur due to thermal expansion, changes in pH, differential swelling, and differential growth. Here we investigate how the presence of both an evolving natural curvature and an external pressure modifies the stability of a complete spherical shell. We show that due to a mechanical analogy between pressure and curvature, positive natural curvatures can severely destabilize a thin shell, while negative natural curvatures can strengthen the shell against buckling, providing the possibility to design shells that buckle at or above the theoretical limit for pressure alone, i.e., a strengthening factor. These results extend directly from the classical analysis of the stability of shells under pressure, and highlight the important role that nonmechanical stimuli can have on modifying the membrane state of stress in a thin shell.
在这项工作中，我们考虑了球壳在均匀外压和均匀自然曲率的联合载荷作用下的稳定性。非机械刺激，例如倾向于改变弹性体静止曲率的刺激，在广泛的自然和工程系统中普遍存在，并且可能由于热膨胀、pH值变化、差异溶胀和差异生长而发生。在这里，我们研究了不断变化的自然曲率和外压的同时存在如何改变完整球壳的稳定性。我们表明，由于压力和曲率之间的力学类比，正的自然曲率会严重破坏薄壳的稳定性，而负的自然曲率可以增强壳抵抗屈曲的能力，从而提供了设计在仅受压力时达到或超过理论极限而屈曲的壳的可能性，即一个强化因子。这些结果直接源于对压力作用下壳稳定性的经典分析，并突出了非机械刺激在改变薄壳膜应力状态方面可能发挥的重要作用。
