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Donati compatibility conditions for membrane and flexural shells

Philippe G. Ciarlet

Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong

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Cristinel Mardare

Université Pierre et Marie Curie, Laboratoire Jacques-Louis Lions, 4 Place Jussieu, 75005 Paris, France

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, and

Xiaoqin Shen

Department of Mathematics, Xi'an University of Technology, Xi'an 710054, P. R. China

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https://doi.org/10.1142/S0219530514500237Cited by:5 (Source: Crossref)

Abstract

Donati compatibility conditions on a surface allow to reformulate the minimization problem for a linearly elastic shell through the intrinsic approach, i.e. as a quadratic minimization problem with the linearized change of metric and change of curvature tensors of the middle surface of the shell as the new unknowns. Such compatibility conditions typically take the form of variational equations with divergence-free tensor fields as test-functions. In a previous work, the first author and Oana Iosifescu have identified and justified Donati compatibility conditions for shells modeled by Koiter's equations. In this paper, Donati compatibility conditions are identified and justified for two specific classes of linearly elastic shells, the so-called elliptic membrane shells and flexural shells.

Keywords:

AMSC: 49J40, 49N10, 74B05, 74K25

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