Linear constrained Cosserat-shell models including terms up to \({O}(h^5)\): conditional and unconditional existence and uniqueness

DOI10.1007/s00033-023-01937-7OpenAlexW4319264801MaRDI QIDQ2681337

Patrizio Neff, Ionel-Dumitrel Ghiba

Publication date: 8 February 2023

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.12074

zbMATH Keywords

curvature measurebending measuredeformation measureconstrained Cosserat elasticitygeometrically nonlinear shell modelminimiser existence

Mathematics Subject Classification ID

Shells (74K25) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (2)

A linear isotropic Cosserat shell model including terms up to \(O(h^5)\). Existence and uniqueness ⋮ A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Saint-Venant's principle in the theory of Cosserat elastic shells
• Finite element approximation of the Navier-Stokes equations
• 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
• Local symmetry group in the general theory of elastic shells
• Thermal stresses in cylindrical cosserat elastic shells
• Elastic materials with couple-stresses
• Existence of weak solutions in linear elastostatics of Cosserat surfaces
• Shells without drilling rotations: a representation theorem in the framework of the geometrically nonlinear 6-parameter resultant shell theory
• On Grioli's minimum property and its relation to Cauchy's polar decomposition
• Refined resultant thermomechanics of shells
• The isotropic Cosserat shell model including terms up to \(O(h^5)\). I: Derivation in matrix notation
• The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers
• On generalized Cosserat-type theories of plates and shells: a short review and bibliography
• Inequalities of Korn's type and existence results in the theory of Cosserat elastic shells
• A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus
• Existence of minimizers in the geometrically non-linear 6-parameter resultant shell theory with drilling rotations
• On the dynamical theory of thermoelastic simple shells
• A mathematical study of the linear theory for orthotropic elastic simple shells
• The Nonlinear Theory of Elastic Shells
• A shell model allowing folds
• Existence and uniqueness for the linear Koiter model for shells with little regularity
• Formulation bidimensionnelle exacte du modèle de coque 3D de Kirchhoff-Love
• Cosserat theories: Shells, rods and points

This page was built for publication: Linear constrained Cosserat-shell models including terms up to \({O}(h^5)\): conditional and unconditional existence and uniqueness