How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements

DOI10.1016/j.cma.2016.10.023zbMath1439.65116OpenAlexW2534441214WikidataQ56669219 ScholiaQ56669219MaRDI QIDQ2308786

Domenico Magisano, Giovanni Garcea, Leonardo Leonetti

Publication date: 3 April 2020

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

Full work available at URL: https://doi.org/10.1016/j.cma.2016.10.023

zbMATH Keywords

finite deformationpath-followinggeometric non-linearitiesintegration pointsMIP Newtondisplacement FE

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22)

Related Items (17)

Unconditional stability in large deformation dynamic analysis of elastic structures with arbitrary nonlinear strain measure and multi-body coupling ⋮ A large rotation finite element analysis of 3D beams by incremental rotation vector and exact strain measure with all the desirable features ⋮ A Koiter reduction technique for the nonlinear thermoelastic analysis of shell structures prone to buckling ⋮ A mixed integration point (MIP) formulation for hyperelastic Kirchhoff-Love shells for nonlinear static and dynamic analysis ⋮ Hourglassing‐ and locking‐free mesh distortion insensitive Petrov–Galerkin EAS element for large deformation solid mechanics ⋮ Deep learned one‐iteration nonlinear solver for solid mechanics ⋮ A dual decomposition of the closest point projection in incremental elasto‐plasticity using a mixed shell finite element ⋮ Large deformation Kirchhoff-Love shell hierarchically enriched with warping: isogeometric formulation and modeling of alternating stiff/soft layups ⋮ A variationally consistent contact formulation based on a mixed interpolation point method and isogeometric discretization ⋮ New robust and efficient global iterations for large deformation finite element analysis of beams and shells with material nonlinearity ⋮ Isogeometric multi-patch analyses for mixed thin shells in the framework of non-linear elasticity ⋮ An isogeometric formulation of the Koiter's theory for buckling and initial post-buckling analysis of composite shells ⋮ Isogeometric analysis for nonlinear planar Kirchhoff rods: weighted residual formulation and collocation of the strong form ⋮ A simplified Kirchhoff-Love large deformation model for elastic shells and its effective isogeometric formulation ⋮ Isogeometric analysis of 3D beams for arbitrarily large rotations: locking-free and path-independent solution without displacement DOFs inside the patch ⋮ A robust penalty coupling of non-matching isogeometric Kirchhoff-Love shell patches in large deformations ⋮ An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells

Cites Work

• Unnamed Item
• New rotation-free finite element shell triangle accurately using geometrical data
• A large displacement and finite rotation thin-walled beam formulation including cross-section deformation
• Nonlinear buckling optimization of composite structures
• Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement
• An incremental approach to the solution of snapping and buckling problems
• Optimal solid shells for nonlinear analyses of multilayer composites. I: Statics.
• The Koiter-Newton approach using von Kármán kinematics for buckling analyses of imperfection sensitive structures
• Mixed formulation and locking in path-following nonlinear analysis
• Extrapolation locking and its sanitization in Koiter's asymptotic analysis
• Families of 4-node and 9-node finite elements for a finite deformation shell theory. An assessment of hybrid stress, hybrid strain and enhanced strain elements
• A robust nonlinear solid shell element based on a mixed variational formulation
• An efficient hybrid/mixed element for geometrically nonlinear analysis of plate and shell structures
• On one-dimensional finite-strain beam theory: the plane problem
• A Koiter-Newton approach for nonlinear structural analysis
• A reduced integration solid-shell finite element based on the EAS and the ANS concept-Large deformation problems
• A corotational interpolatory model for fabric drape simulation
• Path-following analysis of thin-walled structures and comparison with asymptotic post-critical solutions
• An eight-node hybrid-stress solid-shell element for geometric non-linear analysis of elastic shells
• Hybrid hexahedral element for solids, plates, shells and beams by selective scaling
• A numerical analysis of infinitesimal mechanisms
• Mixed formulation in Koiter analysis of thin-walled beams

This page was built for publication: How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements