Approximation of the vibration modes of a plate by Reissner-Mindlin equations

DOI10.1090/S0025-5718-99-01094-7zbMath0945.74030OpenAlexW2023189634WikidataQ58040896 ScholiaQ58040896MaRDI QIDQ4257685

Luis Hervella-Nieto, Ricardo G. Durán, Rodolfo Rodríguez, E. Liberman, Jorge Eduardo Solomin

Publication date: 31 August 1999

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-99-01094-7

zbMATH Keywords

regularityeigenvaluesfinite element approximationeigenfunctionscompact operatorconvergence rateoptimal order of convergencelocking-free methodMITC elements\(H(1)\)-normabstract spectral theorylowest order methodReissner-Mindlin plate bending equationuniform separation of spectrum

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Plates (74K20) Finite element methods applied to problems in solid mechanics (74S05) Numerical approximation of solutions of dynamical problems in solid mechanics (74H15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Finite element linear and nonlinear, static and dynamic analysis of structural elements, an addendum, NONCONFORMING ROTATED ${\mathcal Q}_1$ ELEMENT FOR REISSNER–MINDLIN PLATE, A locking-free Reissner-Mindlin quadrilateral element, Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements, Numerical results for mimetic discretization of Reissner-Mindlin plate problems, Robust Falk-Neilan finite elements for the Reissner-Mindlin plate, Numerical study of the vibrations of an elastic container filled with an inviscid fluid, A locking-free weak Galerkin finite element method for Reissner-Mindlin plate on polygonal meshes, A posteriori error estimator for a mixed finite element method for Reissner-Mindlin plate, Port-Hamiltonian formulation and symplectic discretization of plate models. I: Mindlin model for thick plates, Numerical analysis of a finite element method to compute the vibration modes of a Reissner-Mindlin laminated plate, An alternative alpha finite element method with discrete shear gap technique for analysis of laminated composite plates, The inf-sup condition for low order elements on anisotropic meshes, Finite element analysis of a bending moment formulation for the vibration problem of a non-homogeneous Timoshenko beam

Cites Work

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• Finite element methods (Part 1)
• Design principles and error analysis for reduced-shear plate-bending finite elements
• A four-node plate bending element based on Mindlin/Reissner plate theory and a mixed interpolation
• Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
• A Uniformly Accurate Finite Element Method for the Reissner–Mindlin Plate
• Rayleigh-Ritz vibration analysis of Mindlin plates
• ERROR ANALYSIS OF MIXED-INTERPOLATED ELEMENTS FOR REISSNER-MINDLIN PLATES
• Mixed and Hybrid Finite Element Methods
• Uniform convergence of mixed interpolated elements for Reissner-Mindlin plates
• On Mixed Finite Element Methods for the Reissner-Mindlin Plate Model