Vibration and buckling of laminated plates of complex form under in-plane uniform and non-uniform loading
type: Item
instance of: scholarly article
title: Vibration and buckling of laminated plates of complex form under in-plane uniform and non-uniform loading
zbMATH Open document ID: 1483.74039
DOI: 10.1007/978-3-030-77314-4_21
author: Lidiya Kurpa
author: Victoriya Tkachenko
author: Anna Linnik
publication date: 2022-01-17T00:00:00Z
review text: The vibration and buckling analysis of symmetrically laminated plates with complex form subjected to in-plane uniform and non-uniform loading is performed using variational Ritz's method and the R-functions theory. First-order shear deformation theory of Timoshenko's type is adopted. Each ply is assumed to be an orthotropic homogeneous one without slip at interfaces. The developed approach includes several stages: determination of the heterogeneous subcritical state of the plate; finding buckling critical load; solving linear vibration problem. Ritz's method is applied on each stage. Systems of the admissible functions, that satisfy at least main (kinematic) boundary conditions have been built by the R-functions method. Validation of the proposed method and created software is confirmed by comparison of buckling load and vibration frequency with known results for square laminated plates of free circular or rectangular cut-outs. Buckling loads for laminated clamped plates with complex form under non-uniform edge compressions have been obtained. It is assumed that plates can be made of different materials and have different ply orientations. The effects of the cut-out sizes on critical load and frequency are studied together with the effects of number of layers, degree of orthotropic boundary conditions and type of loading (uniform and non-uniform). There exists many situations when subcritical state of a plate may be inhomogeneous: a plate has cut-out or complex form; external load acting along boundary is non-uniform, and other cases also. The proposed method allows to solve a wide class of similar problems, including plates with cut-outs. Some results obtained by the proposed method are presented. For the entire collection see [Zbl 1477.93111].
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74E30
Mathematics Subject Classification ID: 74S99
zbMATH DE Number: 7457860
zbMATH Keywords: critical buckling load
zbMATH Keywords: laminated plate
zbMATH Keywords: Timoshenko shear deformation theory
zbMATH Keywords: R-function theory
zbMATH Keywords: Rayleigh-Ritz method
reviewed by: Girish Kumar Ramaiah
MaRDI profile type: Publication
full work available at URL: 978-3-030-77314-4 21
OpenAlex ID: W4205501871
cites work: Q3670496
cites work: Q4680129
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description: scientific article; zbMATH DE number 7457860