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A short note on the derivation of the elastic von Kármán shell theory

A short note on the derivation of the elastic von Kármán shell theory We derive the Γ-limit of scaled elastic energies h −4 E h (u h ) associated with deformations u h of a family of thin shells $${S^h} = \left\{ {z = x + t\vec n\left( x \right);x \in S, - g_1^h\left( x \right) < t < g_2^h\left( x \right)} \right\}$$ S h = { z = x + t n → ( x ) ; x ∈ S , − g 1 h ( x ) < t < g 2 h ( x ) } . The obtained von Kármán theory is valid for a general sequence of boundaries g 1 h , g 2 h converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in [10] and [11]. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

A short note on the derivation of the elastic von Kármán shell theory

Acta Mathematicae Applicatae Sinica , Volume 33 (1) – Mar 15, 2017

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References (19)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-017-0640-y
Publisher site
See Article on Publisher Site

Abstract

We derive the Γ-limit of scaled elastic energies h −4 E h (u h ) associated with deformations u h of a family of thin shells $${S^h} = \left\{ {z = x + t\vec n\left( x \right);x \in S, - g_1^h\left( x \right) < t < g_2^h\left( x \right)} \right\}$$ S h = { z = x + t n → ( x ) ; x ∈ S , − g 1 h ( x ) < t < g 2 h ( x ) } . The obtained von Kármán theory is valid for a general sequence of boundaries g 1 h , g 2 h converging to 0 in an appropriate manner as h vanishes. Our analysis relies on the techniques and extends the results in [10] and [11].

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Mar 15, 2017

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