Journal of Elasticity

, Volume 117, Issue 2, pp 163–188

# A New Linear Shell Model for Shells with Little Regularity

• Josip Tambača
Article

## Abstract

In this paper, a new model of linearly elastic shell is formulated. The model is of Koiter’s type capturing the membrane and bending effects. However, the model is well formulated for shells with little regularity, namely the shells whose middle surface is parameterized by a W 1,∞ function.

Unknowns in the model are the displacement $$\tilde{\boldsymbol {u}}$$ of the middle surface of the shell and the infinitesimal rotation $$\tilde{\boldsymbol {\omega}}$$ of the shell cross-section. The existence and uniqueness of the solution of the model has been proved for $$(\tilde{\boldsymbol {u}}, \tilde{\boldsymbol {\omega}}) \in H^{1} \times H^{1}$$ with the help of the Lax-Milgram lemma.

The model is analyzed asymptotically with respect to the small thickness of the shell. It is shown that the model asymptotically behaves just as the membrane model, the flexural model, and the generalized membrane model in each regime. In this way the model is justified.

Since the model is well formulated for shells whose middle surface is with corners, we compare the model with Le Dret’s model of folded plates. It turns out that in the regime of the flexural shells the models are the same. The differential equations of the model are derived. They imply that the model is as a special case of the Cosserat shell model with a single director for a particular constitutive law.

## Keywords

Linear elasticity Shell model Koiter model Little regularity Justification Junctions Folded shells

## Mathematics Subject Classification

74K25 74K30 74K15 74B05

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