Automatic finite element formulation and assembly of hyperelastic higher order structural models

DOI10.1016/J.APM.2013.11.021zbMath1427.74167OpenAlexW2078610938MaRDI QIDQ1630723

Y. Aharonov

Publication date: 10 December 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2013.11.021

zbMATH Keywords

automatic differentiationgeometric nonlinearityhyperelasticityautomatic finite element assemblyautomatic finite element formulationhigher-order structural model

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05)

Related Items (1)

SPINN: sparse, physics-based, and partially interpretable neural networks for PDEs

Uses Software

• DOLFIN
• FEniCS

Cites Work

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• Automatic energy-momentum conserving time integrators for hyperelastic waves
• Highly nonlinear deformation of uniformly-loaded circular plates
• Automatic differentiation: techniques and applications
• On the asymptotic membrane theory of thin hyperelastic plates
• Automatic differentiation of algorithms
• On the derivation of nonlinear rod theories from three-dimensional elasticity
• Transient wave propagation of isotropic plates using a higher-order plate theory
• A general theory of elastic beams
• Higher-order rod approximations for the propagation of longitudinal stress waves in elastic bars
• DOLFIN
• A finite element model for a higher-order shear-deformable beam theory

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