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Aerospace 2018, 5(4), 108; https://doi.org/10.3390/aerospace5040108

Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability

†,* and
Dipartimento di Ingegneria Meccanica e Aerospaziale, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
These authors contributed equally to this work.
*
Author to whom correspondence should be addressed.
Received: 13 September 2018 / Revised: 4 October 2018 / Accepted: 8 October 2018 / Published: 11 October 2018
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Abstract

A number of mixed and displacement-based zig-zag theories are derived from the zig-zag adaptive theory (ZZA). As a consequence of their different assumptions on displacement, strain, and stress fields, and layerwise functions, these theories account for the transverse shear and normal deformability in different ways, but their unknowns are independent of the number of layers. Some have features that are reminiscent of ones that have been published in the literature for the sake of comparison. Benchmarks with different length-to-thickness ratios, lay-ups, material properties, and simply supported or clamped edges are studied with the intended aim of contributing toward better understanding the influence of transverse anisotropy on free vibration and the response of blast-loaded, multilayered, and sandwich plates, as well as enhancing the existing database. The results show that only theories whose layerwise contributions identically satisfy interfacial stress constrains and whose displacement fields are redefined for each layer provide results that are in agreement with elasticity solutions and three-dimensional (3D) finite element analysis (FEA) (mixed solid elements with displacements and out-of-plane stresses as nodal degrees of freedom (d.o.f.)) with a low expansion order of polynomials in the in-plane and out-of-plane directions. The choice of their layerwise functions is shown to be immaterial, while theories with fixed kinematics are shown to be strongly case-sensitive and often inadequate (even for slender components). View Full-Text
Keywords: composite and sandwich plates; zig-zag theories; interlaminar transverse shear and normal stress continuity; Navier’s and 3D finite element analysis (FEA) solutions; free and forced vibrations composite and sandwich plates; zig-zag theories; interlaminar transverse shear and normal stress continuity; Navier’s and 3D finite element analysis (FEA) solutions; free and forced vibrations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Icardi, U.; Urraci, A. Free and Forced Vibration of Laminated and Sandwich Plates by Zig-Zag Theories Differently Accounting for Transverse Shear and Normal Deformability. Aerospace 2018, 5, 108.

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