Buckling of a shell subjected to a probing force

We study the buckling of hemispherical elastic shells subjected to the combined effect of pressure loading and a probing force. We perform an experimental investigation using thin shells of nearly uniform thickness that are fabricated with a well-controlled geometric imperfection. By systematically varying the indentation displacement and the geometry of the probe, we study the effect that the probe-induced deflections have on the buckling strength of our spherical shells. The experimental results are then compared to finite element simulations, as well as to recent theoretical predictions from the literature. Inspired by a nondestructive technique that was recently proposed to evaluate the stability of elastic shells, we characterize the nonlinear load-deflection mechanical response of the probe for different values of the pressure loading. We demonstrate that this nondestructive method is a successful local way to assess the stability of spherical shells.

Related publications:

  • Joel Marthelot, Francisco López-Jiménez, Anna Lee, John W. Hutchinson, and Pedro M. Reis, "Buckling of a Pressurized Hemispherical Shell Subjected to a Probing Force," Journal of Applied Mechanics 84, 121005 (2017).​ [pdf]

Critical buckling pressure of precisely imperfect shells

We study the effect of a dimplelike geometric imperfection on the critical buckling load of spherical elastic shells under pressure loading. This investigation combines precision experiments, finite element modeling, and numerical solutions of a reduced shell theory, all of which are found to be in excellent quantitative agreement. In the experiments, the geometry and magnitude of the defect can be designed and precisely fabricated through a customizable rapid prototyping technique. Our primary focus is on predictively describing the imperfection sensitivity of the shell to provide a quantitative relation between its knockdown factor and the amplitude of the defect. In addition, we find that the buckling pressure becomes independent of the amplitude of the defect beyond a critical value. The level and onset of this plateau are quantified systematically and found to be affected by a single geometric parameter that depends on both the radius-to-thickness ratio of the shell and the angular width of the defect. To the best of our knowledge, this is the first time that experimental results on the knockdown factors of imperfect spherical shells have been accurately predicted, through both finite element modeling and shell theory solutions.

Related publications:

  • Anna Lee, Francisco López-Jiménez, Joel Marthelot, John W. Hutchinson, and Pedro M. Reis, “The Geometric Role of Precisely Engineered Imperfections on the Critical Buckling Load of Spherical Elastic Shells,” Journal of Applied Mechanics 83 (11), 111005 (2016). [pdf]

  • Francisco López-Jiménez, Joel Marthelot, Anna Lee, John W. Hutchinson, and Pedro M. Reis, “Knockdown Factor for the Buckling of Spherical Shells Containing Large-amplitude Geometric Defects,” Journal of Applied Mechanics 84, 034501 (2017). [pdf]


We are interested in understanding the extreme deformation of soft structures and exploring the functionality of mechanical instabilities.

Copyright © Extreme Mechanics Lab, POSTECH. All Rights Reserved.


​Extreme Mechanics Lab, POSTECH

Engineering Building 5, Room 321

77 Cheongam-ro Nam-gu, Pohang-si, Gyeongsangbuk-do

37673, Republic of Korea