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Experimentally probing the stability of thin-shell structures under pure bending

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Philosophical Transactions A
Authors:
Fabien Royer
Fabien Royer
Fabien Royer
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Sergio Pellegrino at California Institute of Technology
Sergio Pellegrino
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Abstract

This paper studies the stability of space structures consisting of longitudinal, open-section thin-shells transversely connected by thin rods subjected to a pure bending moment. Localization of deformation, which plays a paramount role in the nonlinear post-buckling regime of these structures and is extremely sensitive to imperfections, is investigated through probing experiments. As the structures are bent, a probe locally displaces the edge of the thin shells, creating local dimple imperfections. The range of moments for which the early buckling of the structures can be triggered by this perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by a stability landscape, and probing is extended to the entire structure to reveal alternate buckling modes disconnected from the structure’s fundamental path. These results can be used to formulate efficient buckling criteria and pave the way to operating these structures close to their buckling limits, and even in their post-buckling regime, therefore significantly reducing their mass. This article is part of the theme issue ‘Probing and dynamics of shock sensitive shells’.
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Cite this article: Royer F, Pellegrino S. 2023
Experimentally probing the stability of
thin-shell structures under pure bending. Phil.
Trans. R. S oc. A 381: 20220024.
https://doi.org/10.1098/rsta.2022.0024
Received: 5 August 2022
Accepted: 26 October 2022
One contribution of 13 to a theme issue
‘Probing and dynamics of shock sensitive
shells’.
Subject Areas:
structural engineering
Keywords:
pure bending, buckling, thin shells,
imperfection sensitivity, stability landscape
Author for correspondence:
Sergio Pellegrino
e-mail: sergiop@caltech.edu
†Present address: Sibley School of Mechanical
and Aerospace Engineering, Cornell University,
Ithaca, NY 14853, USA.
Experimentally probing the
stability of thin-shell
structures under pure bending
Fabien Royer1,†and Sergio Pellegrino2
1Graduate Aerospace Laboratories, and 2Graduate Aerospace
Laboratories, California Institute of Technology, 1200 E California
Blvd, Pasadena, CA 91125, USA
SP, 0000-0001-9373-3278
This paper studies the stability of space structures
consisting of longitudinal, open-section thin-shells
transversely connected by thin rods subjected to a
pure bending moment. Localization of deformation,
which plays a paramount role in the nonlinear
post-buckling regime of these structures and is
extremely sensitive to imperfections, is investigated
through probing experiments. As the structures are
bent, a probe locally displaces the edge of the thin
shells, creating local dimple imperfections. The range
of moments for which the early buckling of the
structures can be triggered by this perturbation is
determined, as well as the energy barrier separating
the pre-buckling and post-buckling states. The
stability of the local buckling mode is then illustrated
by a stability landscape, and probing is extended
to the entire structure to reveal alternate buckling
modes disconnected from the structure’s fundamental
path. These results can be used to formulate efficient
buckling criteria and pave the way to operating these
structures close to their buckling limits, and even
in their post-buckling regime, therefore significantly
reducing their mass.
This article is part of the theme issue ‘Probing and
dynamics of shock sensitive shells’.
1. Introduction
Thin shell structures are widely used in engineering
applications. They enable lightweight structures of high
stiffness and play a paramount role in the development
of aerospace vehicles. As new applications are proposed
2023 The Author(s) Published by the Royal Society.All rights reser ved.
... Discovering structural response by probing can be an effective technique whether it is conducted experimentally or computationally, as will be evident in the first six papers. The paper by Royer et al. [6] on the ultra-lightweight structures used for supporting solar cell arrays in space employs both experimental and computational probing to reveal the highly complex buckling behaviour of these structures. The following quote from the abstract of this paper succinctly encapsulates the objectives of the technique: 'These results can be used to formulate efficient buckling criteria and pave the way to operating these structures close to their buckling limits, and even in their post-buckling regime, therefore significantly reducing their mass.' ...
... The authors make use of dimensional reduction methods to reduce the nonlinear partial differential equation governing the buckling to a much simpler ordinary differential equation that accurately captures the localization and the progressive loss in bending stiffness. The authors and their co-workers have applied dimensional reduction to other nonlinear systems with great success, and the contribution in this paper should prove useful in modelling systems comprising the shell strip beams such as those employed as the structural elements in the space frames designed for the solar arrays of Royer et al. [6]. ...
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... Chen et al. [9] focused on the buckling of partially supported square plates under uniaxial or biaxial pressures. Royer and Pellegrino [10] examined the static and dynamic mixed mode stress intensity factors of fixed fractures in 2D FGM plates. Czajkowski et al. [11] studied the nonlinear thermal buckling behavior of FGM plates using isogeometric analysis. ...
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