Buckling of Short Beams Considering Shear Warping: Application to Fiber-Reinforced Elastomeric Isolators
Publication: Journal of Engineering Mechanics
Volume 150, Issue 1
Abstract
This paper presents a theory for the buckling of short beams considering cross-sectional distortions due to transverse shear (i.e., shear warping), based on the consistent linearization of a geometrically nonlinear planar beam. The proposed deformation field considers the warping amplitude as an independent kinematic field, and the hyperelastic material assumes that the stresses normal and tangent to the deformed cross section are linear with respect to their work-conjugate finite strains. An approximate closed-form solution to the resulting quartic equation for the critical load is provided to facilitate practical implementation. Theoretical differences giving rise to distinct buckling theories for higher-order shear beams are discussed in terms of (1) the assumed deformation field, (2) variational consistency, and (3) material constitutive relation. The proposed formulation is applied to evaluate the stability of infinite strip unbonded fiber-reinforced elastomeric isolators (FREIs) with moderate-to-high shape factor, for which shear warping is expected to have a major influence due to the flexural flexibility of the fiber reinforcement. A homogenization procedure is described to obtain effective isolator rigidities considering rubber compressibility and fiber extensibility. Next, a finite element parametric study of the buckling of unbonded infinite strip FREIs is presented, and the results are used as a benchmark to evaluate the adequacy of the proposed and existing formulations. The theory presented herein and its approximate solution exhibit the best match with the numerical results, and the latter is deemed adequate for practical application.
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Data Availability Statement
All data, models, and code generated that support the findings of this study are available from the corresponding author upon reasonable request.
Acknowledgments
Comments by Professor Francisco Armero on a draft of the manuscript are appreciated.
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Published In
Journal of Engineering Mechanics
Volume 150 • Issue 1 • January 2024
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Feb 3, 2023
Accepted: Aug 3, 2023
Published online: Oct 18, 2023
Published in print: Jan 1, 2024
Discussion open until: Mar 18, 2024
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Cited by
- Eduardo J. Montalto, Dimitrios Konstantinidis, Effective Warping Properties and Buckling Analysis of Fiber-Reinforced Elastomeric Isolators, Journal of Engineering Mechanics, 10.1061/JENMDT.EMENG-7395, 150, 5, (2024).