Abstract
It is well known that Korn inequality plays a central role in the theory of linear elasticity. In the present work we prove new asymptotically sharp Korn and Korn-like inequalities in thin curved domains with a non-constant thickness. This new results will be useful when studying the buckling of compressed shells, in particular when calculating the critical buckling load.
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Acknowledgements
The present results have been obtained while the author was a postdoctoral fellow at Temple University. The author is very grateful to Y. Grabovsky for supporting his stay at Temple University and for many helpful discussions. He is also thankful to the anonymous reviewer for very valuable comments. The material is based upon work supported by the National Science Foundation Grant No. 1008092 (Y.G.).
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Harutyunyan, D. New Asymptotically Sharp Korn and Korn-Like Inequalities in Thin Domains. J Elast 117, 95–109 (2014). https://doi.org/10.1007/s10659-013-9466-x
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DOI: https://doi.org/10.1007/s10659-013-9466-x