Session: 01-07-01: Nonlinear Problems in Aerospace Structures

Paper Number: 160891

160891 - Quantifying the Effect of Local Imperfections on the Buckling Energy Barrier in Thin-Shell Structures 

The advancement of space technology is closely tied to the development of ultra-lightweight structures, which serve as a foundation for the implementation of larger and more efficient space systems. These developments hold life-changing potential for Earth’s sustainability, particularly through the design of innovative space structures, such as larger space solar power satellites. As the size of these structures increases, so does the generation of clean energy and their contribution to environmental sustainability. Coilable this-shell structures, with their exceptional properties, have enabled lightweight deployable space structures, which, in turn, facilitate the development of large-scale space systems. To realize larger space structures, further development of thin shells is essential, requiring the overcoming of existing limitations and the enhancement of their capabilities. One of the most significant challenges faced by thin-shell structures is their extreme sensitivity to imperfections and external disturbances. Even minor deviations from an ideal geometry can drastically reduce their load-bearing capacity, primarily by diminishing their resistance to buckling. This sensitivity complicates predictions of buckling behaviors, as shells operating near their theoretical buckling limits are prone to collapse unpredictably due to inherent stochastic variations in imperfections. This unpredictable behavior stems from the minimal energy barrier between the pre-buckling and post-buckling states, where even infinitesimal perturbations can trigger early buckling. While traditional approaches to buckling research rely on empirical stochastic methods to establish lower bounds (knockdown factors) for buckling loads, these methods face two critical limitations. First, the results are overly conservative, restricting the performance of thin-shell structures. Second, they require extensive destructive testing that limits scalability and applicability to complex geometries and materials. While early work focused on predicting the buckling load, additional complications arise when trying to predict the post-buckling deformed shape. At the buckling point, the shell undergoes a highly nonlinear process driven by the interaction between global deformations, buckling eigenmodes and imperfections. This phenomenon, known as buckling localization, produces a large number of energetically competing solutions (referred to as spatial chaos), each influenced by a complex interaction between the structure’s theoretical buckling modes and imperfections. Both energy barrier degradation and localization are highly imperfection-sensitive phenomena, which have been shown to contribute to the unpredictability of the buckling behavior and are especially pronounced in structures with lower shell thicknesses. Recent advancements in understanding buckling stability have focused on energy barriers, which quantify the resistance to instability. Recent research introduced a probing methodology to map stability landscapes, enabling the identification of critical buckling energy barriers in pressurized hemispherical shells, coilable ladder structures under bending, cylindrical and spherical shells, circular arches, cylindrical shell roofs and prestressed stayed columns.

In this research, we seek to elucidate the link between local geometric imperfections and buckling energy barriers. Using the same probing methodology, we focus on measuring the buckling energy barrier variation caused by a local dimple imperfection in an open-section semi-circular shell under bending. This type of imperfection has been shown to lead to the earliest transition into buckling (lowest mountain pass point in the energy landscape). These shells are highly sensitive to buckle propagation, with buckling deformation typically localizing at a critical location, allowing for focused study on the effect of a single dimple. Key areas of focus include the variation of energy barriers as a function of the dimple’s aspect ratio, the propagation of localized buckle initiated by the imperfection, and the comparative effects of concave and convex dimples on shell stability. In particular, this study reveals that there exists a critical localization length scale which drives the buckling energy barrier variation and provides a critical imperfection width under which the energy barrier is highly eroded. The main objective of this research is to acquire a more thorough understanding of how to modulate the structural stability of thin-shell structures using localized engineered imperfections.

Presenting Author: Fabien Royer Cornell University

Presenting Author Biography: Fabien is an assistant professor in the Sibley School of Mechanical and Aerospace Engineering at Cornell University. Prior to that he was a Postdoctoral Associate in the Department of Aeronautics and Astronautics at the Massachusetts Institute of Technology. Fabien obtained his MSc and PhD in Space Engineering from Caltech, as well as his Diplôme d’Ingénieur from ISAE-SUPAERO (French national institute for Aeronautics and Space). At Caltech, Fabien worked in Prof. Pellegrino's Space Structures Laboratory where his research focused on ultra-lightweight shell structures, their instabilities, and their application to very large space solar power spacecraft. He also worked on the AAReST (Autonomous Assembly of a Reconfigurable Space Telescope) small satellite mission for which he led part of the spacecraft software and hardware development. In addition to his research, Fabien co-chaired the Caltech Space Challenge 2019, an international student space mission design competition. Fabien was awarded the William F. Ballhaus Prize for outstanding doctoral dissertation by the Caltech Aerospace Department (GALCIT), as well as the Ernest E. Sechler Memorial Award for most significant contribution to the department’s teaching and research effort. In addition, he received the Shirley Thomas Academic Scholarship from the Aerospace Historical Society, and he is a Fellow of the Keck Institute for Space Studies.