Classical and mixed advanced models for sandwich plates embedding functionally graded cores

Abstract

This paper analyzes the bending response of several sandwich plates with a functionally graded core, using advanced equivalent single layer (ESL) and layerwise (LW) models with linear to fourth-order expansion in the thickness direction. The functionally graded properties of the core have been approximated by means of Legendre polynomials. The ESL and LW theories have been developed according to the principle of virtual displacements and Reissner's mixed variational theorem; in the latter case, both displacements and transverse shear/normal stresses have been assumed as primary variables. Closedform solutions for simply supported sandwich plates loaded by a transverse distribution of harmonic pressure are discussed. Various assessments have been made of the proposed theories with respect to the available results. Our obtained results show that, depending on the chosen functionally graded core, the use of advanced models may turn out to be mandatory with respect to classical theories (for example, first-order shear deformation theory). It has been shown that the use of a core in functionally graded material can offer some advantages with respect to the classical cores that have been widely employed in open literature. A benchmark has been proposed which consists of a sandwich plate with two isotropic faces (ceramic and metallic) and various functionally graded cores. That benchmark could be useful in assessing future refined computational models.

Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method

“…To show the convergence of present work, numerical result for dimensionless transverse displacement of sandwich square plate with type B is computed and plotted in Difference between the analytical results and the results presented by Neves et al (2013) and Brischetto (2009) are due to the higher order shear deformation theory (HSDT) used in these references.…”

“…Kant et al (2008) used two-point boundary value problem (BVP) governed by a set of linear first-order ordinary differential equations (ODEs) through the thickness of a laminate to present semi-analytical model for estimation of stresses and displacements in composite and sandwich laminates. Based on classical and mixed advanced models, static analysis of sandwich plates with material properties according to the Legendre polynomials was carried out by Brischetto (2009) According to the comprehensive literature survey, there is no work dealing with the three dimensional static and free vibration characteristics of functionally graded sandwich plates with various edges boundary condition.…”

A review of theories for the modeling and analysis of functionally graded plates and shells

“…Compared to the PVD-based models, the RMVT-based ones give a better prediction of the transverse stresses since they are considered as the primary variables in the RMVT-based models. Brischetto [407] applied the PVD-based models [402] and the RMVT-based models [406] to investigate the bending responses of FG sandwich plates with a FG core. Carrera et al [408] also studied the bending response of FG sandwich plates and shells using the CUF with both PVD-based and RMVT-based models.…”

Refined and Advanced Models for Multilayered Plates and Shells Embedding Functionally Graded Material Layers

“…CUF [24,25], which was originally developed for multilayered anisotropic plates and shells, has been extended to the static mechanical analysis of FGM plates in [28] and [29] using PVD and RMVT variational statements, respectively. Both refined and advanced models have been applied to static sandwich plate analysis in [30], in order to investigate the effects of different FGM cores embedded between a ceramic and a metallic face. The first part of this paper investigates the importance of refined and advanced models for structures embedding FGM layers.…”

“…Then, some benchmarks are proposed to investigate the benefits of introducing some FGM layers into common multilayered or sandwich plates and shells. In addition to the results given in [30], the shell geometry is also investigated and new FGM configurations are considered for the core in sandwich structures.…”