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Published January 14, 2013 | Published
Journal Article Open

Buckling of a cantilever plate uniformly loaded in its plane with applications to surface stress and thermal loads

Abstract

Buckling of elastic structures can occur for loads well within the proportionality limit of their constituent materials. Given the ubiquity of beams and plates in engineering design and application, their buckling behavior has been widely studied. However, buckling of a cantilever plate is yet to be investigated, despite the widespread use of cantilevers in modern technological developments. Here, we address this issue and theoretically study the buckling behavior of a cantilever plate that is uniformly loaded in its plane. Applications of this fundamental problem include loading due to uniform temperature and surface stress changes. This is achieved using a scaling analysis and full three-dimensional numerical solution, leading to explicit formulas for the buckling loads. Unusually, we observe buckling for both tensile and compressive loads, the physical mechanisms for which are explored. We also examine the practical implications of these findings to modern developments in ultra sensitive micro- and nano-cantilever sensors, such as those composed of silicon nitride and graphene.

Additional Information

© 2013 American Institute of Physics. Received 14 September 2012; accepted 4 December 2012; published online 8 January 2013. Online Publication Date: 8 January 2013.The authors gratefully acknowledge support of the Australian Research Council Grants Scheme.

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August 19, 2023
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