Fiorenzo A. Fazzolari

Thermal Stability of FGM Sandwich Plates Under Various Through-the-Thickness Temperature Distributions

A thermal stability analysis of functionally graded material (FGM) isotropic and sandwich plates is carried out by virtue of a refined quasi-3D Equivalent Single Layer (ESL) and Zig-Zag (ZZ) plate models developed within the framework of the Carrera Unified Formulation (CUF) and implemented within the Hierarchical Trigonometric Ritz Formulation (HTRF). The Principle of Virtual Displacements (PVD) is used both to derive the thermal stability differential equations with natural boundary conditions and to develop the HTRF. Uniform, linear, and non-linear temperature rises through-the-thickness direction are taken into account. The non-linear temperature distribution is given in different forms: 1) functionally graded; 2) solution of the one-dimensional Fourier heat conduction equation; and 3) sinusoidal. Several FGM sandwich plate configurations are investigated. Parametric studies are carried out in order to evaluate the effects of significant parameters, such as volume fraction index, length-to-thickness ratio, boundary conditions, aspect ratio, sandwich plate type, and temperature distribution through-the-thickness direction, on the critical buckling temperatures.

Thermo-Mechanical Buckling Analysis of Anisotropic Multilayered Composite and Sandwich Plates by Using Refined Variable-Kinematics Theories

Advanced and refined variable-kinematics plate theories built with a hierarchical approach in an extended framework of Carreras unified formulation (CUF) are combined with Ritz and Galerkin methods to deal with a thermo-mechanical buckling analysis of anisotropic multilayered composite and sandwich plates. Buckling interaction curves and stability envelopes for different thermal and mechanical loading combinations are presented. The influence of the kinematics description and the expansion orders upon the results accuracy is evaluated. The effect of the transverse normal deformation on critical temperature parameters is thoroughly investigated. Convergence and results accuracy are discussed.

Stability analysis of FGM sandwich plates by using variable-kinematics Ritz models

Abstract A linearized buckling analysis of functionally graded material (FGM) isotropic and sandwich plates is carried out by virtue of the Hierarchical Trigonometric Ritz Formulation (HTRF). Quasi-3D Ritz models based on equivalent single layer (ESL) and zig zag (ZZ) plate theories are developed within the framework of the Carrera Unified Formulation (CUF). Several in-plane loading conditions accounting for axial, biaxial, and shear loadings are taken into account. Parametric studies are carried out in order to evaluate the effects of significant parameters, such as volume fraction index, length-to-thickness ratio, sandwich plate type, and loading type, on the critical buckling loads.

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carreras unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

Modal characteristics of P- and S-FGM plates with temperature-dependent materials in thermal environment

ABSTRACT The present article copes with the analysis of free vibration of functionally graded plates with temperature-dependent materials in thermal environment. The functionally graded material (FGM) can be produced by continuously varying the constituents of multiphase materials in a predetermined profile defined by the variation of the volume fraction. In the proposed study, two different volume fractions are considered: (i) power-law function (P-FGM) and (ii) sigmoid function (S-FGM). As the difference between the material properties of the FGM constituents used is relatively small, it is then possible to successfully apply the rule of mixture with no loss of accuracy with respect to the Mori–Tanaka method. The analysis is performed using advanced hierarchical higher order equivalent single-layer plate theories developed using the method of power series expansion of displacement components. The modal characteristics of the P- and S-FGM plates are investigated while subjected to a temperature gradient. More specifically, thermal loadings are induced by the through-the-thickness temperature distribution obtained as the solution of the one-dimensional Fouriers heat conduction equation. The governing equations are derived in their strong form using the principle of the virtual displacements and are solved in an exact sense by using the Navier-type closed form solution. The effect of length-to-thickness ratio, material temperature dependence, and volume fraction index on the natural frequencies is investigated.

Chapter 12 – Thermal buckling

The present chapter provides a comprehensive thermal buckling analysis of laminated composite and sandwich plate structures. Analytical as well as approximate solution methods are used in the investigation. In particular, the Ritz, Galerkin and Generalized Galerkin method are compared. The influence of lamination angle, length-to-thickness ratio and orthotropic ratio on the critical temperature parameter is examined. Finally, the modal characteristics of thermo-mechanically pre/post-buckled anisotropic laminated composite plates are shown.

2 – Sandwich Structures

This chapter provides a comprehensive free vibration and thermal stability analyses of sandwich structures. The analyses are carried out by virtue of advanced and refined variable-kinematic structural models based on the method of power series expansion of displacement components. In particular, in the first part of the chapter classical sandwich structures made up of anisotropic or orthotropic face sheets and honeycomb or foam core are analyzed. The second part is devoted to the investigation of functionally graded material (FGM) sandwich structures. Two different typologies have been taken into account: (1) sandwich structures with FGM core and (2) sandwich structures with FGM face sheets. In this latter case, various configurations, to determine the best FGM sandwich structures in terms of stability characteristics, are also thoroughly examined.

Thermal effect on flutter of panels

This chapter studies the effect of thermomechanical load interactions on the panel flutter phenomena. The classical panel flutter of laminated composite and FGM flat panels is investigated. Aero-thermo-elastic stability diagrams for various panel configurations, different temperatures and dynamic pressure have been obtained.

Multilayered, anisotropic thermal stress structures

This chapter provides various constitutive laws for the most widely used materials in the analysis of thermal structures. In particular, the stress-strain relationships of isotropic, orthotropic, anisotropic and functionally graded materials are proposed. In the latter case, temperature-dependent materials for different types of FGMs are presented. The constitutive law for the RMVT case is also derived. Finally, after defining the Gibbs free-energy and thermo-mechanical enthalpy density, the constitutive equations for thermoelastic problems are obtained.

Through-the-thickness thermal fields in one-layer and multilayered structures

This chapter proposes a thorough thermal stress investigation of layered structures. The temperature profiles and their influence on the static response are evaluated. Stress and displacement fields are computed by accounting for several temperature fields as well as various laminate stacking sequences and geometry. In particular, four sample problems are proposed and the results, obtained by using advanced plate theories, are compared with those available in literature.