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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].
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Mar 15, 2017
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