Benchmark Computations of Stresses in a Spherical Dome with Shell Finite Elements

DOI10.1137/15M1027590zbMath1419.74239arXiv1507.03747OpenAlexW2223099829MaRDI QIDQ2815692

Antti H. Niemi

Publication date: 30 June 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.03747

zbMATH Keywords

convergencefinite elementslockingthin shell theoryshell structuresstabilized methods

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Shells (74K25) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (4)

A DPG method for shallow shells ⋮ Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model ⋮ Natural frequency analysis of shells of revolution based on hybrid dual-mixed \(hp\)-finite element formulation ⋮ Dual-mixed \(hp\)-version axisymmetric shell finite element using NURBS mid-surface interpolation

Uses Software

• Gmsh
• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Application of an automatic \(hp\) adaptive finite element method for thin-walled structures
• The dome and the ring: verification of an old mathematical model for the design of a stiffened shell roof
• An improved treatment of transverse shear in the Mindlin-type four-node quadrilateral element
• The problem of membrane locking in finite element analysis of cylindrical shells
• The first locking-free plane elastic finite element: Historia mathematica
• A stable bilinear element for the Reissner-Mindlin plate model
• Shell deformation states and the finite element method: A benchmark study of cylindrical shells
• Application of a combined continuous-discontinuous Galerkin finite element method for the solution of the Girkmann problem
• Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes
• On the classical shell model underlying bilinear degenerated shell finite elements
• A frontal Delaunay quad mesh generator using theL^∞norm
• The post-processing approach in the finite element method—part 1: Calculation of displacements, stresses and other higher derivatives of the displacements
• Rational approach for assumed stress finite elements
• A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
• A bilinear shell element based on a refined shallow shell model
• Bilinear finite elements for shells: Isoparametric quadrilaterals
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Finite Elements Based Upon Mindlin Plate Theory With Particular Reference to the Four-Node Bilinear Isoparametric Element
• A simple quadrilateral shell element
• Stabilized Finite Element Formulations for Shells in a Bending Dominated State
• Analysis of a bilinear finite element for shallow shells. II: Consistency error
• Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations
• On the classical shell model underlying bilinear degenerated shell finite elements: general shell geometry
• Locking-free finite element methods for shells

This page was built for publication: Benchmark Computations of Stresses in a Spherical Dome with Shell Finite Elements