Closed and approximate analytical solutions for rectangular Mindlin plates

DOI10.1007/BF01182359zbMath1014.74046OpenAlexW2051595338MaRDI QIDQ5942649

Holm Altenbach, Konstantin Naumenko, V. K. Naumenko, Johannes Altenbach

Publication date: 21 July 2003

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01182359

zbMATH Keywords

infinite seriesexact solutiondifferential equationsrectangular platesprinciple of virtual displacementsapproximate analytical solutionboundary layer solutionsMindlin's plate equationsNádai-Lévy methodVlasov-Kantorovich methods

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Plates (74K20) Explicit solutions of equilibrium problems in solid mechanics (74G05)

Related Items (9)

Exact solutions for the in-plane vibrations of rectangular Mindlin plates using Helmholtz decomposition ⋮ Higher-order hybrid stress triangular Mindlin plate element ⋮ Effective heat conductivity of a composite with hexagonal lattice of perfectly conducting circular inclusions: An analytical solution ⋮ Subclasses of Mechanical Problems Arising from the Direct Approach for Homogeneous Plates ⋮ A non-classical Mindlin plate model based on a modified couple stress theory ⋮ Free vibration analysis of plates taking into account rotary inertia and shear deformation via three alternative theories: a Lévy-type solution ⋮ On the use of the first order shear deformation plate theory for the analysis of three-layer plates with thin soft core layer ⋮ Laminated Plates with Non-linear Visco-elastic Interlayer: The Governing Equations ⋮ Solution to bending problem of trapezoid composite laminates

Uses Software

• ANSYS

Cites Work

• Differential cubature method for static solutions of arbitrarily shaped thick plates
• On the problem of shear-locking in finite elements based on shear deformable plate theory
• A simplified analysis of rectangular cellular plates
• An alternative determination of transverse shear stiffness for sandwich and laminated plates
• An application of the extended Kantorovich method to the stress analysis of a clamped rectangular plate
• An extended Kantorovich method for the solution of eigenvalue problems
• Deflection and stress-resultants of axisymmetric Mindlin plates in terms of corresponding Kirchhoff solutions
• On the analysis of thick rectangular plates
• Green's function applied to solution of mindlin plates
• An extension of the Kantorovich method
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