Finite element simulation of nonlinear bending models for thin elastic rods and plates

DOI10.1016/BS.HNA.2019.06.003zbMath1455.35255arXiv1901.09835OpenAlexW2913729386MaRDI QIDQ3300076

Sören Bartels

Publication date: 27 July 2020

Published in: Geometric Partial Differential Equations - Part I (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.09835

zbMATH Keywords

convergenceelasticityfinite element methodsiterative solutionnonlinear bending

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Plates (74K20) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) PDEs in connection with mechanics of deformable solids (35Q74) Finite volume methods applied to problems in solid mechanics (74S10) Energy minimization in dynamical problems in solid mechanics (74H80)

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Discontinuous Galerkin approach to large bending deformation of a bilayer plate with isometry constraint ⋮ A descent scheme for thick elastic curves with self-contact and container constraints ⋮ A nonlinear bending theory for nematic LCE plates ⋮ Specht Triangle Approximation of Large Bending Isometries ⋮ Derivation of a homogenized bending-torsion theory for rods with micro-heterogeneous prestrain ⋮ Numerical solution of a bending-torsion model for elastic rods ⋮ Theories for incompressible rods: A rigorous derivation via Γ-convergence ⋮ Computing confined elasticae

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