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Variational Formulation and Symmetric Tangent Operator for Shells with Finite Rotation Field

Yoshitaka Suetake1, Masashi Iura2, S. N. Atluri3

AIT, Ashikaga, Tochigi, JAPAN
TDU, Hikigun, Saitama, JAPAN
UC Irvine, Irvine, CA, U.S.A

Computer Modeling in Engineering & Sciences 2003, 4(2), 329-336. https://doi.org/10.3970/cmes.2003.004.329

Abstract

The objective of this paper is to examine the symmetry of the tangent operator for nonlinear shell theories with the finite rotation field. As well known, it has been stated that since the rotation field carries the Lie group structure, not a vector space one, the tangent operator incorporating the rotation field does not become symmetric. In this paper, however, it is shown that by adopting a rotation vector as a variable, the symmetry can be achieved in the Lagrangean (material) description. First, we present a general concept for the problem. Next, we adopt the finitely deformed thick shell problem as an example. We also present a tensor formula that plays a key role for the derivation of a symmetric tangent operator.

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Suetake, Y., Iura, M., Atluri, S. N. (2003). Variational Formulation and Symmetric Tangent Operator for Shells with Finite Rotation Field. CMES-Computer Modeling in Engineering & Sciences, 4(2), 329–336. https://doi.org/10.3970/cmes.2003.004.329



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