Formulation bidimensionnelle exacte du modèle de coque 3D de Kirchhoff-Love

Anicic, Sylvia; Léger, Alain

doi:10.1016/s0764-4442(00)88228-2

Cited by 17 publications

(10 citation statements)

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“…Moreover, the assumptions which follow from considering µ c → ∞ are also expressed naturally in terms of 3), see estimate (3.63) and Section 3.2. This line of thought, beside some other arguments presented in the linearised framework by Anicic and Léger [6], see also [3], and more recently by Šilhavỳ [39], suggest that the triple G ∞ , R ∞ − 2 G ∞ L y0 and K ∞ are appropriate measures to express the change of metric and of the curvatures H and K, while the bending and drilling effects are both additionally incorporated in the bending-curvature energy through the elastic shell bending-curvature tensor K ∞ .…”

Section: Strain Measures In the Cosserat Shell Modelmentioning

confidence: 65%

“…Since E s = Q T e,s F e,s − 1 3 , this condition is equivalent to: the Biot-type stretch tensor U e,s = Q T e,s F e,s for the 3D shell is symmetric. In conclusion, from (3.27) we see that the tensor (E m,s B y0 + C y0 K e,s ) can be viewed as a bending tensor for shells in the sense of Anicic and Léger [6] and Šilhavỳ [39].…”

Section: D Versus 2d Symmetry Requirements For µ C → ∞mentioning

confidence: 86%

“…Contrary to other 6-parameter theory of shells [36,12,19,13] the membrane-bending energy is expressed in terms of the specific tensor E m,s B y0 + C y0 K e,s . This tensor represents a nonlinear change of curvature tensor, since in the linear constrained Cosserat model [22] it reduces to the change of curvature tensor considered by Anicic and Léger [6] and more recently by Šilhavỳ [39].…”

Section: The Unconstrained Cosserat Shell Modelmentioning

confidence: 99%

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A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

Ghiba,

Bîrsan,

Lewintan

et al. 2020

Preprint

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We consider a recently introduced geometrically nonlinear elastic Cosserat shell model incorporating effects up to order O(h 5 ) in the shell thickness h. We develop the corresponding geometrically nonlinear constrained Cosserat shell model, we show the existence of minimizers for the O(h 5 ) and O(h 3 ) case and we draw some connections to existing models and classical shell strain measures. Notably, the role of the appearing new bending tensor is highlighted and investigated with respect to an invariance condition of Acharya [Int. J. Solids and Struct., 2000] which will be further strengthened.

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Section: Strain Measures In the Cosserat Shell Modelmentioning

confidence: 65%

Section: D Versus 2d Symmetry Requirements For µ C → ∞mentioning

confidence: 86%

Section: The Unconstrained Cosserat Shell Modelmentioning

confidence: 99%

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A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

Ghiba,

Bîrsan,

Lewintan

et al. 2020

Preprint

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“…Even though the formulation of this model is initially three-dimensional, it can be shown that the model is nonetheless two-dimensional. The two-dimensional formulation is however quite complicated, see [5] and [2].…”

Section: Lemma 55 If γ C Is Nonempty or γ S Is Not Included In A Strmentioning

confidence: 99%

WELL-POSEDNESS FOR KOITER AND NAGHDI SHELLS WITH A G₁-MIDSURFACE

Dret

2004

Anal. Appl.

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“…The tensor ε is used standardly for the Kirchoff-Love deformations. The tensor ρ AL , called the Anicic-Léger bending strain tensor in this paper, was introduced by Anicic & Léger in [2], independently of ρ D , but their motivation is different. The resulting asymptotics is…”

Section: Introductionmentioning

confidence: 99%

A new approach to curvature measures in linear shell theories

Šilhavý

2020

Mathematics and Mechanics of Solids

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The paper presents a coordinate-free analysis of deformation measures for shells modeled as 2D surfaces. These measures are represented by second-order tensors. As is well-known, two types are needed in general: the surface strain measure (deformations in tangential directions), and the bending strain measure (warping). Our approach first determines the 3D strain tensor E of a shear deformation of a 3D shell-like body and then linearizes E in two smallness parameters: the displacement and the distance of a point from the middle surface. The linearized expression is an affine function of the signed distance from the middle surface: the absolute term is the surface strain measure and the coefficient of the linear term is the bending strain measure. The main result of the paper determines these two tensors explicitly for general shear deformations and for the subcase of Kirchhoff-Love deformations. The derived surface strain measures are the classical ones: Naghdi’s surface strain measure generally and its well-known particular case for the Kirchhoff-Love deformations. With the bending strain measures comes a surprise: they are different from the traditional ones. For shear deformations our analysis provides a new tensor [Formula: see text], which is different from the widely used Naghdi’s bending strain tensor [Formula: see text]. In the particular case of Kirchhoff–Love deformations, the tensor [Formula: see text] reduces to a tensor [Formula: see text] introduced earlier by Anicic and Léger (Formulation bidimensionnelle exacte du modéle de coque 3D de Kirchhoff–Love. C R Acad Sci Paris I 1999; 329: 741–746). Again, [Formula: see text] is different from Koiter’s bending strain tensor [Formula: see text] (frequently used in this context). AMS 2010 classification: 74B99

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Formulation bidimensionnelle exacte du modèle de coque 3D de Kirchhoff-Love

Cited by 17 publications

References 1 publication

A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

WELL-POSEDNESS FOR KOITER AND NAGHDI SHELLS WITH A G₁-MIDSURFACE

A new approach to curvature measures in linear shell theories

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Formulation bidimensionnelle exacte du modèle de coque 3D de Kirchhoff-Love

Cited by 17 publications

References 1 publication

A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

A constrained Cosserat shell model up to order $O(h^5)$: Modelling, existence of minimizers, relations to classical shell models and scaling invariance of the bending tensor

WELL-POSEDNESS FOR KOITER AND NAGHDI SHELLS WITH A G1-MIDSURFACE

A new approach to curvature measures in linear shell theories

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WELL-POSEDNESS FOR KOITER AND NAGHDI SHELLS WITH A G₁-MIDSURFACE