Abstract
We derive the Γ-limit of scaled elastic energies h−4Eh(uh) associated with deformations uh of a family of thin shells \({S^h} = \left\{ {z = x + t\vec n\left( x \right);x \in S, - g_1^h\left( x \right) < t < g_2^h\left( x \right)} \right\}\) . The obtained von Kármán theory is valid for a general sequence of boundaries g h1 , g h2 converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in [10] and [11].
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Acknowledgements
I also want to thank Professor Marta Lewicka for her advice and guidance during the work.
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This research was partially supported by Professor Marta Lewicka’s NSF grants DMS-0707275 and DMS-0846996 and by her Polish MN grant N N201 547438.
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Li, H. A short note on the derivation of the elastic von Kármán shell theory. Acta Math. Appl. Sin. Engl. Ser. 33, 93–106 (2017). https://doi.org/10.1007/s10255-017-0640-y
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DOI: https://doi.org/10.1007/s10255-017-0640-y