scholarly journals Toward Variability Characterization and Statistic Models’ Constitution for the Prediction of Exponentially Graded Plates’ Static Response

2018 ◽  
Vol 2 (4) ◽  
pp. 59 ◽  
Author(s):  
Rafael Rosa ◽  
Maria Loja ◽  
Alda Carvalho
Keyword(s):  
Prediction Models ◽  
Shear Deformation Theory ◽  
Sampling Technique ◽  
Latin Hypercube Sampling ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Functionally Graded Composite ◽  
Static Responses ◽  
Graded Material ◽  
Exponentially Graded

Functionally graded composite materials may constitute an advantageous alternative to engineering applications, allying a customized tailoring capability to its inherent continuous properties transition. However, these attractive characteristics must account for the uncertainty that affects these materials and their structures’ physical quantities. Therefore, it is important to analyze how this uncertainty will modify the foreseen deterministic response of a structure that is built with these materials, identifying which of the parameters are responsible for a greater impact. To pursue this main objective, the material and geometrical parameters that characterize a plate made of an exponentially graded material are generated according to a random multivariate normal distribution, using the Latin hypercube sampling technique. Then, a set of finite element analyses based on the first-order shear deformation theory are performed to characterize the linear static responses of these plates, which are further correlated to the input parameters. This work also considers the constitution of statistic models in order to allow their use as alternative prediction models. The results show that for the plates that were analyzed, the uncertainty associated with the elasticity modulus of both phases is mainly responsible for the maximum transverse deflection variability. The effectiveness of the statistical models that are built are also shown.

scholarly journals Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 2: Numerical results and discussion

2017 ◽  
Vol 39 (4) ◽  
pp. 329-338
Author(s):  
Dang Thuy Dong ◽  
Dao Van Dung
Keyword(s):  
Elastic Foundation ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Shallow Shells ◽  
Nonlinear Dynamic Equations ◽  
Graded Material ◽  
Doubly Curved

In part 1, the governing nonlinear dynamic equations of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners on elastic foundation subjected to mechanical and thermal loading are established based on the first order shear deformation theory (FSDT) with von Kármán - type nonlinearity and smeared stiffener technique. In the present part, the fourth-order Runge-Kutta method is applied to investigate influences of models of the shells, FGM stiffeners, thermal environment, elastic foundation, and geometrical parameters on the natural frequencies and dynamic nonlinear responses of stiffened FGM sandwich doubly curved shallow shells.

Bending Analysis of Piezoelectric Functionally Graded Material Plates Using HSDT

2019 ◽  
Vol 969 ◽  
pp. 116-121
Author(s):  
Ch. Naveen Reddy ◽  
M. Bhargav ◽  
T. Revanth
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Graded Material

This work investigates the complete analytical solution for functionally graded material (FGM) plates incorporated with smart material. The odjective of the present work is to determine bending characteristics of piezoelectric FGM plates with different geometrical parameters, voltages and boundary conditions for electro-mechanical loading. In this work an analytical formulation based on higher order shear deformation theory (HSDT) is presented for the piezoelectric FGM plates. The solutions are obtained in closed from using Navier’s technique for piezoelectric FGM plates a specific type of simply supported boundary conditions and pc code have been developed to find out the deflections and stresses for various parameters. All the solutions are plotted against aspect proportion, side to thickness proportion as a function of material variety parameter (n) and thickness coordinate for different voltages. The significant trends from the results are obtained.

scholarly journals Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

2014 ◽  
Vol 229 (5) ◽  
pp. 818-839 ◽  
Author(s):  
A Asanjarani ◽  
S Satouri ◽  
A Alizadeh ◽  
MH Kargarnovin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Conical Shell ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Graded Material ◽  
Truncated Conical Shell

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

Thermal Post-Buckling Analysis of Functionally Graded Composite Plates with Nonlinear Aerodynamic Forces

2010 ◽  
Vol 123-125 ◽  
pp. 280-283
Author(s):  
Chang Yull Lee ◽  
Ji Hwan Kim
Keyword(s):  
Material Properties ◽  
Numerical Solutions ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Functionally Graded Composite ◽  
Post Buckling

The post-buckling of the functionally graded composite plate under thermal environment with aerodynamic loading is studied. The structural model has three layers with ceramic, FGM and metal, respectively. The outer layers of the sandwich plate are different homogeneous and isotropic material properties for ceramic and metal. Whereas the core is FGM layer, material properties vary continuously from one interface to the other in the thickness direction according to a simple power law distribution in terms of the volume fractions. Governing equations are derived by using the principle of virtual work and numerical solutions are solved through a finite element method. The first-order shear deformation theory and von-Karman strain-displacement relations are based to derive governing equations of the plate. Aerodynamic effects are dealt by adopting nonlinear third-order piston theory for structural and aerodynamic nonlinearity. The Newton-Raphson iterative method applied for solving the nonlinear equations of the thermal post-buckling analysis

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

TSDT theory for free vibration of functionally graded plates with various material properties

2021 ◽  
Vol 8 (4) ◽  
pp. 691-704
Author(s):  
M. Janane Allah ◽  
◽  
Y. Belaasilia ◽  
A. Timesli ◽  
A. El Haouzi ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Volume Fraction ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Implicit Algorithm ◽  
Proposed Model ◽  
Graded Material ◽  
Composite Modeling

In this work, an implicit algorithm is used for analyzing the free dynamic behavior of Functionally Graded Material (FGM) plates. The Third order Shear Deformation Theory (TSDT) is used to develop the proposed model. In this contribution, the formulation is written without any homogenization technique as the rule of mixture. The Hamilton principle is used to establish the resulting equations of motion. For spatial discretization based on Finite Element Method (FEM), a quadratic element with four and eight nodes is adopted using seven degrees of freedom per node. An implicit algorithm is used for solving the obtained problem. To study the accuracy and the performance of the proposed approach, we present comparisons with literature and laminate composite modeling results for vibration natural frequencies. Otherwise, we examine the influence of the exponent of the volume fraction which reacts the plates "P-FGM" and "S-FGM". In addition, we study the influence of the thickness on "E-FGM" plates.

TiN/Al2O3 Functionally Graded Material Fabricated by In Situ Reaction

2008 ◽  
Vol 368-372 ◽  
pp. 1835-1837
Author(s):  
Jian Hua Nie ◽  
Ya Wei Li ◽  
Hao Yan ◽  
Yong He Liang ◽  
Yuan Bing Li
Keyword(s):  
Phase Composition ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Initial Reaction ◽  
Tio2 Powder ◽  
Functionally Graded Composite ◽  
Epma Analysis ◽  
Graded Material ◽  
Al Powder

TiN/Al2O3 functionally graded composite was fabricated by in-situ aluminothermic reduction of TiO2 in coke bed from mixtures of TiO2 powder and metal Al powder. The reaction process, phase composition, and microstructure of sample treated at 1500°C for 3h were analyzed by XRD, SEM and EPMA. The results indicated that the thermite reduction of TiO2 involves several transitional stages and its initial reaction temperature is lowered by prior reaction between Al and TiO2. EPMA analysis showed that the TiN/Al2O3 ratio in TiN/Al2O3 functionally graded material products changes gradually across the samples without distinct interface between the different layers. The microstructure of the composite changes gradually, and the size of TiN grains increases from the verge region of samples to the centre of samples. These results above were in agreement with thermodynamic analysis.

Influence of coupled fields on free vibration and static behavior of functionally graded magneto-electro-thermo-elastic plate

2017 ◽  
Vol 29 (7) ◽  
pp. 1430-1455 ◽  
Author(s):  
Vinyas Mahesh ◽  
Piyush J Sagar ◽  
Subhaschandra Kattimani
Keyword(s):  
Finite Element ◽  
Electric Fields ◽  
Elastic Plate ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Finite Element Formulation ◽  
Geometrical Parameters ◽  
Element Formulation ◽  
Elastic Plates

In this article, the influence of full coupling between thermal, elastic, magnetic, and electric fields on the natural frequency of functionally graded magneto-electro-thermo-elastic plates has been investigated using finite element methods. The contribution of overall coupling effect as well as individual elastic, piezoelectric, piezomagnetic, and thermal phases toward the stiffness of magneto-electro-thermo-elastic plates is evaluated. A finite element formulation is derived using Hamilton’s principle and coupled constitutive equations of magneto-electro-thermo-elastic material. Based on the first-order shear deformation theory, kinematics relations are established and the corresponding finite element model is developed. Furthermore, the static studies of magneto-electro-elastic plate have been carried out by reducing the fully coupled finite element formulation to partially coupled state. Particular attention has been paid to investigate the influence of thermal fields, electric fields, and magnetic fields on the behavior of magneto-electro-elastic plate. In addition, the effect of pyrocoupling on the magneto-electro-elastic plate has also been studied. Furthermore, the effect of geometrical parameters such as aspect ratio, length-to-thickness ratio, stacking sequence, and boundary conditions is studied in detail. The investigation may contribute significantly in enhancing the performance and applicability of functionally graded magneto-electro-thermo-elastic structures in the field of sensors and actuators.

Bending and free vibration analyses of functionally graded material nanoplates via a novel nonlocal single variable shear deformation plate theory

2020 ◽  
pp. 095440622096452
Author(s):  
Le Kha Hoa ◽  
Pham Van Vinh ◽  
Nguyen Dinh Duc ◽  
Nguyen Thoi Trung ◽  
Le Truong Son ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Functionally Graded Material ◽  
Numerical Solutions ◽  
Scale Effects ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Small Scale ◽  
Parameter Study ◽  
Graded Material

A novel nonlocal shear deformation theory is established to investigate functionally graded nanoplates. The significant benefit of this theory is that it consists of only one unknown variable in its displacement formula and governing differential equation, but it can take into account both the quadratic distribution of the shear strains and stresses through the plate thickness as well as the small-scale effects on nanostructures. The numerical solutions of simply supported rectangular functionally graded material nanoplates are carried out by applying the Navier procedure. To indicate the accuracy and convergence of this theory, the present solutions have been compared with other published results. Furthermore, a deep parameter study is also carried out to exhibit the influence of some parameters on the response of the functionally graded material nanoplates.

scholarly journals A Non-Intrusive Stochastic Isogeometric Analysis of Functionally Graded Plates with Material Uncertainty

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 92
Author(s):  
Shaima M. Dsouza ◽  
Tittu Mathew Varghese ◽  
P. R. Budarapu ◽  
S. Natarajan
Keyword(s):  
Zirconium Oxide ◽  
Isogeometric Analysis ◽  
Deformation Theory ◽  
Polynomial Chaos ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
B Splines ◽  
First Order ◽  
Graded Material

A non-intrusive approach coupled with non-uniform rational B-splines based isogeometric finite element method is proposed here. The developed methodology was employed to study the stochastic static bending and free vibration characteristics of functionally graded material plates with inhered material randomness. A first order shear deformation theory with an artificial shear correction factor was used for spatial discretization. The output randomness is represented by polynomial chaos expansion. The robustness and accuracy of the framework were demonstrated by comparing the results with Monte Carlo simulations. A systematic parametric study was carried out to bring out the sensitivity of the input randomness on the stochastic output response using Sobol’ indices. Functionally graded plates made up of Aluminium (Al) and Zirconium Oxide (ZrO2) were considered in all the numerical examples.

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