The isotropic Cosserat shell model including terms up to \(O(h^5)\). II: Existence of minimizers

DOI10.1007/s10659-020-09795-4zbMath1456.49040arXiv2003.08594OpenAlexW3092128185MaRDI QIDQ2224460

Ionel-Dumitrel Ghiba, Mircea Bîrsan, Patrizio Neff, Peter Lewintan

Publication date: 3 February 2021

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.08594

zbMATH Keywords

dimensional reductionuniform convexitycalculus of variationsisotropydislocation density tensorexistence of minimizersthin structureswryness tensor6-parameter resultant shellgeometrically nonlinear Cosserat shellin-plane drill rotations

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Plates (74K20) Shells (74K25) Existence theories for free problems in two or more independent variables (49J10) Micromechanical theories (74A60) Variational principles of physics (49S05) Applications of functional analysis to differential and integral equations (46N20)

Related Items (9)

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 ⋮ On solvability of initial boundary-value problems of micropolar elastic shells with rigid inclusions ⋮ A linear isotropic Cosserat shell model including terms up to \(O(h^5)\). Existence and uniqueness ⋮ A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elements ⋮ Linear constrained Cosserat-shell models including terms up to \({O}(h^5)\): conditional and unconditional existence and uniqueness ⋮ Hilbert complexes: analysis, applications, and discretizations. Abstracts from the workshop held June 19--25, 2022 ⋮ A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence ⋮ The isotropic Cosserat shell model including terms up to \(O(h^5)\). I: Derivation in matrix notation ⋮ Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

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