On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results

This paper presents a new inverse tangent shear deformation theory (ITSDT) for the static, free vibration and buckling analysis of laminated composite and sandwich plates. In the present theory, shear stresses are vanished at the top and bottom surfaces of the plates and shear correction factors are no longer required. A weak form of the static, free vibration and buckling models for laminated composite and sandwich plates based on ITSDT is then derived and is numerically solved using an isogeometric analysis (IGA). The proposed formulation requires C1-continuity generalized displacements and hence basis functions used in IGA fulfill this requirement. Numerical examples are provided to show high efficiency of the present method compared with other published solutions.

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Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory

This study investigates and reviews approaches to modelling laminated composite plates. It explores theories that have been proposed and developed and assesses their suitability and functionality. The particular focus in this study has been on normal stresses and the through-thickness distributions of transverse shear. These are important for composite plates as stress-induced failures can occur in three different ways. Therefore, it is essential to understand and calculate transverse shear and normal stress through the thickness of the plate accurately. In this study, previous laminated composite plate theories are categorised and reviewed in a general sense, i.e. not problem specific, and the advantages and disadvantages of each model are discussed. This research mainly focuses on how accurate and efficient the models can predict the transverse shear. It starts with displacement-based theories from very basic models such as Classical laminate plate theory to more complicated and higher-order shear deformation theory. Models are furthermore categorised by how the models consider the overall laminate. In this article, the theories are divided into two parts: Single layer theory, where the whole plate is considered as one layer; and Layerwise theory, where each layer is treated separately. The models based on zig-zag and Discrete Theories are then reviewed, and finally the mixed (hybrid) plate theories are studied.

The development of laminated composite plate theories: a review

We present in this paper a simple and effective formulation based on a fifth-order shear deformation theory (FiSDT) in combination with isogeometric finite element analysis (IGA) for composite sandwich plates. The FiSDT yields non-linear distribution of the transverse shear stresses through the plate thickness and ensures a prior tangential stress-free boundary condition. The IGA uses same basis functions, namely B-splines or non-uniform rational B-splines (NURBS), for preserving the precisely geometric representation and providing the numerical solution. It enables to achieve easily the smoothness with arbitrary continuity order and in the present method the C1-continuity requirement of higher order shear deformation models is fulfilled. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical examples are given to show high accuracy of the proposed method.

Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory

https://imechanica.org/files/Exact%20characteristic%20equations%20for%20some%20of%20classical%20boundary%20conditions%20of%20vibrating%20moderately%20thick%20rectangular%20plates.pdf

Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates

Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model

Linear analysis of laminated composite plates using single layer higher-order discrete models

This paper presents a parametric study of the free vibrations of square plates with various thickness‐to‐span ratios and different boundary conditions. The numerical analysis of these problems has been undertaken using the finite element method. In particular, a nine‐noded, quadrilateral Mindlin plate element has been adopted. The effects of rotatory inertia and shear deformation are included in this model. Results obtained by the finite element analysis are compared with results from various sources. It is suggested that this study might be used to supplement existing benchmark tests.

Dj. Vuksanović

Papers

Bending, free vibrations and buckling of laminated composite and sandwich plates using a layerwise displacement model

Linear analysis of laminated composite plates using single layer higher-order discrete models

Free vibrations of Mindlin plates using the finite element method: Part 1. Square plates with various edge conditions