Combined influence of shallowness and geometric imperfection on the buckling of clamped spherical shells

We investigate the combined influence of shallowness and geometric imperfection on the pressure-induced buckling behavior of clamped spherical shells. The buckling phenomenon in spherical shells has gained significant interest in diverse fields, such as soft robotics and biomechanics, due to its distinct and drastic shape morphing characteristics. However, a notable discrepancy between analytic solutions and experimental results persists, necessitating further research to comprehend the buckling behavior of spherical shells with varying shallowness and geometric imperfection. To address this gap, we experimentally investigate the buckling of clamped spherical shells under uniform pressure while controlling the shell shallowness over a wide range. The experimental results validate finite element simulations, enabling analysis of the variation in buckling pressure and behaviors by manipulating the shell shallowness and geometric imperfection. Our analysis reveals decaying oscillatory variations in the buckling strength versus the shallowness curves, eventually converging to stable buckling strength for sufficiently deep shells. Moreover, these curves exhibit changes in level and shape with varying geometric imperfection. We also observe non-axisymmetric buckling modes in shells with small geometric imperfection and specific shallowness ranges. Through parametric studies, we identify the geometric conditions influencing the buckling behavior, particularly the non-snap-through criteria and non-axisymmetric buckling modes. This comprehensive investigation sheds light on the interplay between shallowness and geometric imperfection affecting the buckling behavior of clamped spherical shells. The findings contribute to a deeper understanding of shell buckling phenomena and have implications for various shell design applications.