AN ANALYTICAL APPROACH FOR BUCKLING BEHAVIOR OF TEMPERATURE-DEPENDENT LAMINATED PIEZOELECTRIC FUNCTIONALLY GRADED PLATES UNDER THERMO-ELECTRO-MECHANICAL LOADINGS AND DIFFERENT END SUPPORTS

2014 ◽  
Vol 11 (04) ◽  
pp. 1350099 ◽  
Author(s):  
ABDOLHOSSEIN FEREIDOON ◽  
HESSAMEDDIN YAGHOOBI ◽  
ALI DEHGHANIAN
Keyword(s):  
Analytical Approach ◽  
Volume Fraction ◽  
Plate Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Buckling Behavior ◽  
Parametric Studies ◽  
Plate Aspect Ratio ◽  
Fgm Layer

In this paper, we examine the buckling behavior of piezoelectric laminated plate made of two-layered functionally graded materials (FGMs) that are integrated with surface-bonded piezoelectric actuators and is subjected to a combined action of uniform temperature change, inplane forces, and applied actuator voltage. Temperature-dependent material properties are assumed for both the substrate FGM layer and piezoelectric layers. Employing an analytical approach, five coupled governing stability equations, which were derived based on the first-order shear deformation plate theory, are converted into a fourth-order and a second-order decoupled partial differential equations. Then, an accurate analytical solution is proposed to solve them. Parametric studies are also undertaken, and show the effects of applied actuator voltage, volume fraction exponents, plate aspect ratio, ratio of piezoelectric layer thickness to thickness of FGM layer and temperature dependency, on the buckling load of the plate.

Designing Optimal Volume Fractions For Functionally Graded Materials With Temperature-Dependent Material Properties

2006 ◽  
Vol 74 (5) ◽  
pp. 861-874 ◽  
Author(s):  
Florin Bobaru
Keyword(s):  
Functionally Graded Materials ◽  
Material Properties ◽  
Volume Fraction ◽  
Effective Properties ◽  
Functionally Graded ◽  
Dominant Factor ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Critical Stresses ◽  
Non Linear

We present a numerical approach for material optimization of metal-ceramic functionally graded materials (FGMs) with temperature-dependent material properties. We solve the non-linear heterogeneous thermoelasticity equations in 2D under plane strain conditions and consider examples in which the material composition varies along the radial direction of a hollow cylinder under thermomechanical loading. A space of shape-preserving splines is used to search for the optimal volume fraction function which minimizes stresses or minimizes mass under stress constraints. The control points (design variables) that define the volume fraction spline function are independent of the grid used in the numerical solution of the thermoelastic problem. We introduce new temperature-dependent objective functions and constraints. The rule of mixture and the modified Mori-Tanaka with the fuzzy inference scheme are used to compute effective properties for the material mixtures. The different micromechanics models lead to optimal solutions that are similar qualitatively. To compute the temperature-dependent critical stresses for the mixture, we use, for lack of experimental data, the rule-of-mixture. When a scalar stress measure is minimized, we obtain optimal volume fraction functions that feature multiple graded regions alternating with non-graded layers, or even non-monotonic profiles. The dominant factor for the existence of such local minimizers is the non-linear dependence of the critical stresses of the ceramic component on temperature. These results show that, in certain cases, using power-law type functions to represent the material gradation in FGMs is too restrictive.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

Characteristics of Power Law and Sigmoid FGMs Models in Thermal Effect

2016 ◽  
Vol 829 ◽  
pp. 90-94
Author(s):  
Seok Hyeon Kang ◽  
Ji Hwan Kim
Keyword(s):  
Power Law ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Virtual Work ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Virtual Work Principle ◽  
Temperature Dependent Properties

In thermal environment, vibration behavior of Functionally Graded Materials (FGMs) plates is investigated, and the materials are developed with mixing ceramic and metal. Present study is based on the first-order shear deformation theory of plate. Then, mixture methods such as Power law (P-) and Sigmoid (S-) models are chosen. According to a volume fraction, the material properties are assumed to vary continuously through the thickness direction and to be temperature dependent properties. Further, thermal effects are considered as uniform temperature rise and one dimensional heat transfer. For the structure analysis, FEM is used to obtain the natural frequencies based on the virtual work principle.

FREE VIBRATION AND BUCKLING OF FUNCTIONALLY GRADED SHELL PANELS IN THERMAL ENVIRONMENTS

2010 ◽  
Vol 10 (05) ◽  
pp. 1031-1053 ◽  
Author(s):  
S. PRADYUMNA ◽  
J. N. BANDYOPADHYAY
Keyword(s):  
Free Vibration ◽  
Compressive Load ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Temperature Dependent ◽  
Graded Materials ◽  
Thermal Environments ◽  
Buckling Behavior ◽  
Doubly Curved

This paper investigates the free vibration and buckling behavior of singly and doubly curved shell panels made of functionally graded materials (FGMs). A higher-order shear deformation theory is used for the analysis of five shell panels, namely, cylindrical (CYL), spherical (SPH), hyperbolic paraboloid (HPR), hypar (HYP), and conoid (CON). The shell panels are subjected to a temperature field and in the case of buckling analysis, the shell panels are also subjected to a uniaxial compressive load. The properties of FGMs are considered to be temperature dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The accuracy of the formulation is validated by comparing the results with those available in the literature. The effects of geometric properties, material composition, and boundary conditions on the free vibration and buckling are studied.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Buckling Behavior of FG-CNT Reinforced Composite Conical Shells Subjected to a Combined Loading

Nanomaterials ◽  
2020 ◽  
Vol 10 (3) ◽  
pp. 419 ◽  
Author(s):  
Abdullah H. Sofiyev ◽  
Francesco Tornabene ◽  
Rossana Dimitri ◽  
Nuri Kuruoglu
Keyword(s):  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Structural Response ◽  
Systematic Investigation ◽  
Functionally Graded ◽  
Combined Loading ◽  
Proportional Loading ◽  
Conical Shells ◽  
Reinforced Composite ◽  
Buckling Behavior

The buckling behavior of functionally graded carbon nanotube reinforced composite conical shells (FG-CNTRC-CSs) is here investigated by means of the first order shear deformation theory (FSDT), under a combined axial/lateral or axial/hydrostatic loading condition. Two types of CNTRC-CSs are considered herein, namely, a uniform distribution or a functionally graded (FG) distribution of reinforcement, with a linear variation of the mechanical properties throughout the thickness. The basic equations of the problem are here derived and solved in a closed form, using the Galerkin procedure, to determine the critical combined loading for the selected structure. First, we check for the reliability of the proposed formulation and the accuracy of results with respect to the available literature. It follows a systematic investigation aimed at checking the sensitivity of the structural response to the geometry, the proportional loading parameter, the type of distribution, and volume fraction of CNTs.

Torsional vibration of functionally graded carbon nanotube reinforced conical shells

2018 ◽  
Vol 25 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Yaser Kiani
Keyword(s):  
Torsional Vibration ◽  
Conical Shell ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Coupled Equations ◽  
Parametric Studies ◽  
Torsional Frequency ◽  
Generalized Differential

AbstractThe present study deals with the free torsional vibration of a composite conical shell made of a polymeric matrix reinforced with carbon nanotubes (CNTs). Distribution of CNTs across the thickness of the conical shell may be uniform or functionally graded. Five different cases of functionally graded reinforcements are considered. First-order shear deformable shell theory compatible with the Donnell kinematic assumptions is used to establish the motion equations of the shell. These equations are two coupled equations which should be treated as an eigenvalue problem. The generalized differential quadrature method is used to obtain a numerical solution for the torsional frequency parameters and the associated mode shapes of the shell. After validating the results of this study for the cases of isotropic homogeneous cone and annular plates, parametric studies are carried out to analyze the influences of geometrical characteristics of the shell, volume fraction of CNTs, and grading profile of the CNTs. It is shown that volume fraction of CNTs is an important factor with regard to torsional frequencies of the shell; however, grading profile does not change the torsional frequencies significantly.

Solidification Processing of Functionally Graded Materials by Sedimentation

1999 ◽  
Author(s):  
J. W. Gao ◽  
S. J. White ◽  
C. Y. Wang
Keyword(s):  
Functionally Graded Materials ◽  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Computer Code ◽  
Functionally Graded ◽  
Particle Volume ◽  
Particle Sedimentation ◽  
Graded Materials ◽  
Free Zone ◽  
Free Region

Abstract A combined experimental and numerical investigation of the solidification process during gravity casting of functionally graded materials (FGMs) is conducted. Focus is placed on the interplay between the freezing front propagation and particle sedimentation. Experiments were performed in a rectangular ingot using pure substances as the matrix and glass beads as the particle phase. The time evolutions of local particle volume fractions were measured by bifurcated fiber optical probes working in the reflection mode. The effects of various processing parameters were explored. It is found that there exists a particle-free zone in the top portion of the solidified ingot, followed by a graded particle distribution region towards the bottom. Higher superheat results in slower solidification and hence a thicker particle-free zone and a higher particle concentration near the bottom. The higher initial particle volume fraction leads to a thinner particle-free region. Lower cooling temperatures suppress particle settling. A one-dimensional solidification model was also developed, and the model equations were solved numerically using a fixed-grid, finite-volume method. The model was then validated against the experimental results, and the validated computer code was used as a tool for efficient computational prototyping of an Al/SiC FGM.

Chaotic Motion of a Functionally Graded Materials Square Thin Plate

2012 ◽  
Vol 531 ◽  
pp. 593-596
Author(s):  
Shuang Bao Li ◽  
Yu Xin Hao
Keyword(s):  
Thin Plate ◽  
Functionally Graded Materials ◽  
Chaotic Motion ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Third Order ◽  
Graded Materials ◽  
Steady State Heat ◽  
Steady State Heat Transfer

Chaotic motion of a simply supported functionally graded materials (FGM) square thin plate under one-to-two internal resonance is studied in this paper. The FGM plate is subjected to the transversal and in-plane excitations. Material properties are assumed to be temperature-dependent and change continuously throughout the thickness of the plate. The temperature variation is assumed to occur in the thickness direction only and satisfy the steady-state heat transfer equation. Based on the Reddy’s third-order plate theory and Hamilton’s principle, the nonlinear governing equations of motion for the FGM plate are derived by using the Galerkin’s method to describe the transverse oscillation in the first two modes Numerical simulations illustrate that there exist chaotic motion for the FGM rectangular plate.

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