A geometrically nonlinear Cosserat shell model for orientable and non-orientable surfaces: discretization with geometric finite elements

DOI10.1016/j.cma.2023.116309arXiv2304.11329MaRDI QIDQ6084443

Lisa Julia Nebel, Oliver Sander, Mircea Bîrsan, Patrizio Neff

Publication date: 6 November 2023

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2304.11329

zbMATH Keywords

existencenon-orientablegeometrically nonlineargeometric finite elementselastic Cosserat shellnonplanar reference configuration

Mathematics Subject Classification ID

Shells (74K25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Cites Work

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• Numerical treatment of a geometrically nonlinear planar Cosserat shell model
• An algorithm to compute the polar decomposition of a \(3 \times 3\) matrix
• Assumed-metric spherically interpolated quadrilateral shell element
• Isogeometric Reissner-Mindlin shell analysis with exactly calculated director vectors
• On natural strain measures of the non linear micropolar continuum
• On a stress resultant geometrically exact shell model. I: Formulation and optimal parametrization
• The interpolation of rotations and its application to finite element models of geometrically exact rods
• Elastic theory of unconstrained non-Euclidean plates
• Twist buckling and the foldable cylinder: an exercise in origami
• Optimal a priori discretization error bounds for geodesic finite elements
• Algebraic topology
• Metrics for 3D rotations: comparison and analysis
• A three-dimensional finite-strain rod model. II. Computational aspects
• Nonlinear finite element analysis of shells. I. Three-dimensional shells
• A nonlinear composite shell element with continuous interlaminar shear stresses
• On Grioli's minimum property and its relation to Cauchy's polar decomposition
• \(L^{2}\)-discretization error bounds for maps into Riemannian manifolds
• Treatment of Reissner-Mindlin shells with Kinks without the need for drilling rotation stabilization in an isogeometric framework
• On a stress resultant geometrically exact shell model. III: Computational aspects of the nonlinear theory
• Newton's method, zeroes of vector fields, and the Riemannian center of mass
• The Cosserat surface as a shell model, theory and finite element formulation
• On the parametrization of finite rotations in computational mechanics. A classification of concepts with application to smooth shells
• Alternative derivation of the higher-order constitutive model for six-parameter elastic shells
• Calculus of variations on thin prestressed films. Asymptotic methods in elasticity (to appear)
• A large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable features
• The \textsc{Dune} framework: basic concepts and recent developments
• 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
• A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
• Grioli's theorem with weights and the relaxed-polar mechanism of optimal Cosserat rotations
• A geometrically exact Cosserat shell model for defective elastic crystals. Justification via \(\Gamma\)-convergence
• 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
• Quasi-interpolation in Riemannian manifolds
• Geodesic finite elements on simplicial grids
• FEM analysis of Cosserat plates and shells based on some constitutive relations
• Differentiable Piecewise-Bézier Surfaces on Riemannian Manifolds
• Geometric Finite Elements
• Shell curvature as an initial deformation: A geometrically exact finite element approach
• Geodesic finite elements for Cosserat rods
• Constraint preserving implicit finite element discretization of harmonic map flow into spheres
• Probability, Convexity, and Harmonic Maps with Small Image I: Uniqueness and Fine Existence
• Riemannian center of mass and mollifier smoothing
• Thin shells with finite rotations formulated in biot stresses: Theory and finite element formulation
• The Nonlinear Theory of Elastic Shells
• Objectivity of strain measures in the geometrically exact three-dimensional beam theory and its finite-element implementation
• Iterative Computation of the Fréchet Derivative of the Polar Decomposition
• Embedding-Based Interpolation on the Special Orthogonal Group
• Projection-Based Finite Elements for Nonlinear Function Spaces
• Frame-indifferent beam finite elements based upon the geometrically exact beam theory
• Geometry, analysis, and morphogenesis: Problems and prospects
• Refined dimensional reduction for isotropic elastic Cosserat shells with initial curvature
• Derivation of a refined six-parameter shell model: descent from the three-dimensional Cosserat elasticity using a method of classical shell theory
• DUNE — The Distributed and Unified Numerics Environment
• Polar Decomposition and Matrix Sign Function Condition Estimates
• CONVERGENCE OF A FINITE ELEMENT DISCRETIZATION FOR THE LANDAU–LIFSHITZ EQUATIONS IN MICROMAGNETISM
• A GEOMETRICALLY EXACT PLANAR COSSERAT SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO COSSERAT COUPLE MODULUS
• Some Metric Inequalities in the Space of Matrices
• Measure and integration theory
• Finite elements. Theory, fast solvers and applications in elasticity theory
• A geometrically nonlinear Cosserat (micropolar) curvy shell model via gamma convergence

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