Analysis of a bilinear finite element for shallow shells I: Approximation of inextensional deformations

DOI10.1090/S0025-5718-01-01376-XzbMath0999.74109MaRDI QIDQ4529702

Juhani Pitkäranta, Ville Havu

Publication date: 6 May 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

lockingerror boundconvergence rateenergy normparabolic shellhyperbolic shellelliptic shellbilinear reduced-strain finite element formulationinextensional displacement fieldshallow shell of Reissner-Naghdi type

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Shells (74K25) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Approximation of shell layers using bilinear elements on anisotropically refined rectangular meshes, Cell-centered nonlinear finite-volume methods for the heterogeneous anisotropic diffusion problem, Benchmark computations on point-loaded shallow shells: Fourier vs. FEM, Bilinear finite elements for shells: Isoparametric quadrilaterals, 3D-SHELL ELEMENTS AND THEIR UNDERLYING MATHEMATICAL MODEL, Analysis of a bilinear finite element for shallow shells. II: Consistency error, AN INTERPOLATION THEORY APPROACH TO SHELL EIGENVALUE PROBLEMS, A Reduction Approximation Method for Curved Rods, Benchmark Computations of Stresses in a Spherical Dome with Shell Finite Elements

Cites Work

• The problem of membrane locking in finite element analysis of cylindrical shells
• Shell deformation states and the finite element method: A benchmark study of cylindrical shells
• A formulation of general shell elements—the use of mixed interpolation of tensorial components
• Fundamental considerations for the finite element analysis of shell structures
• A benchmark study of reduced-strain shell finite elements: quadratic schemes
• On the classical shell model underlying bilinear degenerated shell finite elements: general shell geometry
• Fourier mode analysis of layers in shallow shell deformations