The Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Part I: Derivation in Matrix Notation

Ghiba, Ionel–Dumitrel; Bîrsan, Mircea; Lewintan, Peter; Neff, Patrizio

doi:10.1007/s10659-020-09796-3

Cited by 18 publications

(50 citation statements)

References 80 publications

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“…The quadratic representation (150) has been adopted also in the work [5], where a model of order O(h 3 ) for Cosserat shells has been derived. Thus, using the same derivation method and the conditions (151), we have obtained in [5, f. (68)] the strain energy densityW shell (E e , K e ) in the form (28) Next, let us compare our results with the shell model obtained in [7], see also the work [18] which presents this model in matrix formulation. In [7, f. (65)], the following quadratic ansatz has been assumed…”

Section: Special Case: the Quadratic Ansatzmentioning

confidence: 90%

Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Bîrsan

2021

Z. Angew. Math. Phys.

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In this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

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Section: Special Case: the Quadratic Ansatzmentioning

confidence: 90%

Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Bîrsan

2021

Z. Angew. Math. Phys.

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“…Naghdi-type shell models with only one independent "Cosserat"-director do not have the drill-degree of freedom [27] but allow for transverse shear. Classical shell models neither have drill nor transverse shear [19,15,36]. On the contrary, rotations about in-plane axis describe bending and twist.…”

Section: Engineering Motivation: Cosserat Shell Modelsmentioning

confidence: 99%

“…The extension of the planar shell model to initially curved shells has been recently given in [18,19,20]. The planar shell model (1.9) has been used to successfully predict the wrinkling behavior of very thin elastic sheets [37].…”

Section: Engineering Motivation: Cosserat Shell Modelsmentioning

confidence: 99%

On in-plane drill rotations for Cosserat surfaces

Saem,

Lewintan,

Neff

2021

Preprint

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We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a C 2 -smooth regular shell surface to another one parametrized over the same domain are impossible provided that the rotations are fixed at a portion of the boundary. Put otherwise, if the tangent vectors of the new surface are obtained locally by only rotating the given tangent vectors, and if these rotations have a rotation axis which coincides everywhere with the normal of the initial surface, then the two surfaces are equal provided they coincide at a portion of the boundary. In the language of differential geometry of surfaces we show that any isometry which leaves normals invariant and which coincides with the given surface at a portion of the boundary, is the identity mapping.

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“…The extension of the planar shell model to initially curved shells has been recently given in [31,34,35]. The planar shell model (1.8) has been used to successfully predict the wrinkling behaviour of very thin elastic sheets [36].…”

Section: Introductionmentioning

confidence: 99%

On in-plane drill rotations for Cosserat surfaces

2021

Self Cite

View full text Add to dashboard Cite

We show under some natural smoothness assumptions that pure in-plane drill rotations as deformation mappings of a C 2 -smooth regular shell surface to another one parametrized over the same domain are impossible provided that the rotations are fixed at a portion of the boundary. Put otherwise, if the tangent vectors of the new surface are obtained locally by only rotating the given tangent vectors, and if these rotations have a rotation axis which coincides everywhere with the normal of the initial surface, then the two surfaces are equal provided they coincide at a portion of the boundary. In the language of differential geometry of surfaces, we show that any isometry which leaves normals invariant and which coincides with the given surface at a portion of the boundary is the identity mapping.

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The Isotropic Cosserat Shell Model Including Terms up to $O(h^{5})$. Part I: Derivation in Matrix Notation

Cited by 18 publications

References 80 publications

Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

On in-plane drill rotations for Cosserat surfaces

On in-plane drill rotations for Cosserat surfaces

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