A mathematical analysis of the simplest direct models for rods and shells

DOI10.1007/BF01055752zbMath0697.73001OpenAlexW1967504145MaRDI QIDQ911830

N. E. Zubov

Publication date: 1989

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01055752

zbMATH Keywords

diskreversibleshellrodlocal modelsnon-reversibleautomorphisms of a diskbundle of filamentsconcept of material symmetryCosserats directorsglobal modelsone-dimensional set of disksstack of planestwo-dimensional set of disks

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids (74-02) Membranes (74K15)

Related Items (8)

A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS ⋮ Local symmetry group in the general theory of elastic shells ⋮ Homogeneous monotropic elastic rods: Normal uniform configurations and universal solutions ⋮ A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence ⋮ On a finite disk method for hyperelastic rods and shells ⋮ On generalized Cosserat-type theories of plates and shells: a short review and bibliography ⋮ A LARGE DEFORMATION, VISCOELASTIC, THIN ROD MODEL: DERIVATION AND ANALYSIS ⋮ 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

Cites Work

• On the applicability of directed fluid jets to Newtonian and non-Newtonian flows
• Materially uniform simple bodies with inhomogeneities
• On the geometric structures of simple bodies, a mathematical foundation for the theory of continuous distributions of dislocations
• Material uniformity and homogeneity in shells
• On the theory of rods. I. Derivations from the three-dimensional equations
• Directed fluid sheets
• Nonlinear Theory of Elastic Surfaces

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