Analysis of some low-order finite element schemes for Mindlin-Reissner and Kirchhoff plates

DOI10.1007/BF01395887zbMath0654.73043OpenAlexW1536407545MaRDI QIDQ1108852

Juhani Pitkäranta

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133274

zbMATH Keywords

triangulationerror estimateslow-order finite element schemesmesh dependent energy normthree degrees of freedom

Mathematics Subject Classification ID

Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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Studies in plate flexure. I: A mixed finite element formulation for Reissner-Mindlin plate theory: Uniform convergence of all higher-order spaces, A locking-free Reissner-Mindlin quadrilateral element, Wilson's element for the Reissner-Mindlin plate, A stable bilinear element for the Reissner-Mindlin plate model, A mixed finite element for shell model with free edge boundary conditions. I: The mixed variational formulation. II: The numerical scheme, A multigrid method for a parameter dependent problem in solid mechanics, Avoiding locking in Reissner-Mindlin plates with high-order hierarchic bubble plus finite elements, Uniform analysis of a stabilized hybrid finite element method for Reissner-Mindlin plates, Regular decomposition and a framework of order reduced methods for fourth order problems, On finite element formulations for the obstacle problem -- mixed and stabilised methods, A New Approach to Reduce Transverse Shear Locking of Reissner–Mindlin Plate Based on The Cell-Centered Finite Element Method, Mixed and nonconforming finite element approximations of Reissner-Mindlin plates., A finite element method with discontinuous rotations for the Mindlin-Reissner plate model, A priori and a posteriori analysis for a locking-free low order quadrilateral hybrid finite element for Reissner-Mindlin plates, An additive Schwarz method for plate bending problems, Analysis of a mixed finite element method for the Reissner-Mindlin plate problems, A multigrid method for Reissner-Mindlin plates, Stable Mixed Element Schemes for Plate Models on Multiply-Connected Domains, \(h\)-and \(d\)-adaptive FE methods for two-dimensional structural problems including post-buckling of shells, The problem of membrane locking in finite element analysis of cylindrical shells, Stabilized finite element methods. II: The incompressible Navier-Stokes equations, Analysis of kinematic linked interpolation methods for Reissner-Mindlin plate problems, Analysis of the discontinuous Petrov-Galerkin method with optimal test functions for the Reissner-Mindlin plate bending model, Analysis of mixed finite elements for laminated composite plates, Two lower order nonconforming rectangular elements for the Reissner-Mindlin plate, Locking-free finite elements for the Reissner-Mindlin plate, On the convergence of a mixed finite element method for Reissner-Mindlin plates, PARTIAL SELECTIVE REDUCED INTEGRATION SCHEMES AND KINEMATICALLY LINKED INTERPOLATIONS FOR PLATE BENDING PROBLEMS, Analysis of some low order quadrilateral Reissner-Mindlin plate elements, A stable mixed element method for the biharmonic equation with first-order function spaces, Superconvergence and postprocessing of MITC plate elements, Hierarchical models of thin elastic structures: overview and recent advances in error estimation and adaptivity, Shell deformation states and the finite element method: A benchmark study of cylindrical shells, An improved Reissner-Mindlin triangular element, A finite element method for Reissner-Mindlin plates

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