scholarly journals Response of Functionally Graded Material Plate under Thermomechanical Load Subjected to Various Boundary Conditions

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Manish Bhandari ◽  
Kamlesh Purohit
Keyword(s):  
High Temperature ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Shear Deformation Theory ◽  
Light Metal ◽  
Functionally Graded ◽  
Numerical Results ◽  
Element Formulation ◽  
Power Law Distribution

Functionally graded materials (FGMs) are one of the advanced materials capable of withstanding the high temperature environments. The FGMs consist of the continuously varying composition of two different materials. One is an engineering ceramic to resist the thermal loading from the high-temperature environment, and the other is a light metal to maintain the structural rigidity. In the present study, the properties of the FGM plate are assumed to vary along the thickness direction according to the power law distribution, sigmoid distribution, and exponential distribution. The fundamental equations are obtained using the first order shear deformation theory and the finite element formulation is done using minimum potential energy approach. The numerical results are obtained for different distributions of FGM, volume fractions, and boundary conditions. The FGM plate is subjected to thermal environment and transverse UDL under thermal environment and the response is analysed. Numerical results are provided in nondimensional form.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

2019 ◽  
Vol 233 (10) ◽  
pp. 2140-2159 ◽  
Author(s):  
Ehsan Arshid ◽  
Ali Kiani ◽  
Saeed Amir
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Sensors And Actuators

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach

2017 ◽  
Vol 232 (18) ◽  
pp. 3235-3249 ◽  
Author(s):  
Nitin Sharma ◽  
Trupti Ranjan Mahapatra ◽  
Subrata Kumar Panda
Keyword(s):  
Boundary Element ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Acoustic Radiation ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Higher Order ◽  
Element Formulation ◽  
Present Scheme ◽  
Acoustic Responses

In this article, the vibration-induced acoustic responses of laminated composite flat panels subjected to harmonic mechanical excitation under uniform temperature load are investigated numerically. The natural frequencies alongside corresponding modes of the flat panels resting on an infinite rigid baffle are obtained by using finite element method in the framework of the higher-order shear deformation theory. A coupled finite and boundary element formulation is then employed to acquire the acoustic responses. The governing equation for the sound radiaiton from the vibrating structures is derived by solving the Helmholtz wave equation. The vibration and acoustic responses are computed by using the present scheme via an in-house computer code developed in MATLAB environment. In order to avoid any excess thermal loading conditions first, the critical buckling temperature of the panel structure is obtained and authenticated with the benchmark values. Further, the sound power levels for isotropic and laminated composite panels are computed using the present scheme and validated with the existing results in the published literature. Finally, the influence of lamination scheme, support conditions and modular ratio on the acoustic radiation behavior of laminated composite flat panels in an elevated thermal environment is studied through various numerical examples. The thermal load is found to have substantial influence on the stiffness of the panels and the peaks in the free vibration responses tend to shift to lower frequencies for higher temperatures. It is also inferred that the panels radiate less efficiently whereas the overall sound pressure level is found to follow an increasing trend with increasing temperature.

Effect of Porosity on Flexural Vibration of CNT-Reinforced Cylindrical Shells in Thermal Environment Using GDQM

2018 ◽  
Vol 18 (10) ◽  
pp. 1850123 ◽  
Author(s):  
Hamed Safarpour ◽  
Kianoosh Mohammadi ◽  
Majid Ghadiri ◽  
Mohammad M. Barooti
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Cylindrical Shells ◽  
Flexural Vibration ◽  
Distribution Patterns ◽  
Functionally Graded ◽  
Equivalent Material

This article investigates the flexural vibration of temperature-dependent and carbon nanotube-reinforced (CNTR) cylindrical shells made of functionally graded (FG) porous materials under various kinds of thermal loadings. The equivalent material properties of the cylindrical shell of concern are estimated using the rule of mixture. Both the cases of uniform distribution (UD) and FG distribution patterns of reinforcements are considered. Thermo-mechanical properties of the cylindrical shell are supposed to vary through the thickness and are estimated using the modified power-law rule, by which the porosities with even and uneven types are approximated. As the porosities occur inside the FG materials during the manufacturing process, it is necessary to consider their impact on the vibration behavior of shells. The present study is featured by consideration of different types of porosities in various CNT reinforcements under various boundary conditions in a single model. The governing equations and boundary conditions are developed using Hamilton's principle and solved by the generalized differential quadrature method. The accuracy of the present results is verified by comparison with existing ones and those by Navier's method. The results show that the length to radius ratio and temperature, as well as CNT reinforcement, porosity, thermal loading, and boundary conditions, play an important role on the natural frequency of the cylindrical shell of concern in thermal environment.

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.

scholarly journals Thermoelastic stability of thick imperfect functionally graded plates

2010 ◽  
Vol 32 (1) ◽  
pp. 47-58 ◽  
Author(s):  
Hoang Van Tung ◽  
Nguyen Dinh Duc
Keyword(s):  
Shear Deformation ◽  
Thermal Loading ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Functionally Graded Plate ◽  
Closed Form Solutions ◽  
Geometrical Imperfection ◽  
Nonlinear Temperature

This paper investigates buckling of thick functionally graded plates with initial geometrical imperfection under thermal loadings. The equilibrium, stability, and compatibility equations of an imperfect functionally graded plate are derived using the third order shear deformation theory. Material properties are assumed to be temperature-independent and graded in the thickness direction according to a simple power law distribution in terms of the thickness coordinate variable. By Galerkin method, the resulting equations are solved to obtain closed-form solutions of critical buckling temperature difference. Two types of thermal loading, uniform temperature rise and nonlinear temperature change across the thickness are considered. Buckling analysis for a simply supported rectangular imperfect functionally graded plate shows effects of geometry and material parameters, shear deformation and imperfection on critical buckling temperature.

Nonlinear Dynamics of FGM Conical Panel With Initial Imperfection in Thermal Environment

2017 ◽  
Author(s):  
Ming Hui Yao ◽  
Yan Niu ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Thermal Environment ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Initial Imperfection ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Phase Portraits ◽  
Power Law Distribution ◽  
Geometric Imperfection

In this paper, the nonlinear dynamics of a simply supported functionally graded materials (FGM) conical panel with different forms of initial imperfections is investigated. The conical panel is subjected to the simple harmonic excitation along the radial direction and the parametric excitation in the meridian direction. The small initial geometric imperfection of the conical panel is expressed by the form of the Cosine functions. According to a power-law distribution, the effective material properties are assumed to be graded along the thickness direction. Based on the first-order shear deformation theory and von Karman type nonlinear geometric relationship, the nonlinear equations of motion are established by using the Hamilton principle. The nonlinear partial differential governing equations are truncated by Galerkin’s method to obtain the ordinary differential equations along the radial displacement. The effects of imperfection types, half-wave numbers and amplitudes on the dynamic behaviors are studied by numerical simulation. Maximum Lyapunov exponents, bifurcation diagrams, time histories and phase portraits are obtained to show the dynamic response.

scholarly journals Large deformation behavior of functionally graded porous curved beams in thermal environment

2021 ◽  
Author(s):  
S. F. Nikrad ◽  
A. Kanellopoulos ◽  
M. Bodaghi ◽  
Z. T. Chen ◽  
A. Pourasghar
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Bending Moment ◽  
Functionally Graded ◽  
Equilibrium Path ◽  
Curved Beams ◽  
Governing Equations

AbstractThe in-plane thermoelastic response of curved beams made of porous materials with different types of functionally graded (FG) porosity is studied in this research contribution. Nonlinear governing equations are derived based on the first-order shear deformation theory along with the nonlinear Green strains. The nonlinear governing equations are solved by the aid of the Rayleigh–Ritz method along with the Newton–Raphson method. The modified rule-of-mixture is employed to derive the material properties of imperfect FG porous curved beams. Comprehensive parametric studies are conducted to explore the effects of volume fraction and various dispersion patterns of porosities, temperature field, and arch geometry as well as boundary conditions on the nonlinear equilibrium path and stability behavior of the FG porous curved beams. Results reveal that dispersion and volume fraction of porosities have a significant effect on the thermal stability path, maximum stress, and bending moment at the crown of the curved beams. Moreover, the influence of porosity dispersion and structural geometry on the central radial and in-plane displacement of the curved beams is evaluated. Results show that various boundary conditions make a considerable difference in the central radial displacements of the curved beams with the same porosity dispersion. Due to the absence of similar results in the specialized literature, this paper is likely to provide pertinent results that are instrumental toward a reliable design of FG porous curved beams in thermal environment.

Influence of Material Uncertainty on Vibration Characteristics of Higher-Order Cracked Functionally Gradient Plates Using XFEM

2021 ◽  
Vol 13 (05) ◽  
Author(s):  
Ahmed Raza ◽  
Mohammad Talha ◽  
Himanshu Pathak
Keyword(s):  
Perturbation Technique ◽  
Shear Deformation Theory ◽  
Partition Of Unity ◽  
Higher Order ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Level Set Function

In this study, the influence of material uncertainty on the vibration characteristics of the cracked functionally graded materials (FGM) plates is investigated. Extended stochastic finite element formulation is implemented to model the cracked FGM plate with material uncertainty using higher-order shear deformation theory (HSDT). The level set function is employed to track the crack in the FGM domain. The concept of partition of unity technique is implemented to enrich the primary variable with additional functions. The gradation of the material properties along the thickness direction is done using the power-law distribution. The first-order perturbation technique (FOPT) is incorporated in the methodology for stochastic vibration analysis. The convergence and validation study has been performed to verify the efficacy and accuracy of the formulation. Numerical results are obtained to show the effects of various influential parameters like crack length, gradient index, thickness ratio, and boundary condition on the covariance of the square of natural frequencies. The presented computational approach is accurate, efficient, and robust enough to investigate the vibration response of cracked FGM plates with material randomness.

Nonlinear Free Vibration of Piezoelectric Functionally Graded Beams in Thermal Environment

2015 ◽  
Author(s):  
Ali Fallah ◽  
Mohammad Taghi Ahmadian ◽  
Ahmad Barari
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Nonlinear Behavior ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Functionally Graded ◽  
Nonlinear Free Vibration ◽  
Simple Analytical Expression

Nonlinear free vibration analysis of piezoelectric functionally graded (PFG) beams in thermal environment with any boundary conditions are investigated. The nonlinear governing Equation of motion is derived based on the Euler-Bernoulli beam theory and Von Karman’s strain-displacement relation. Simple analytical expression is presented for the nonlinear natural frequency using energy balanced method (EBM). Results are validated and compared with available results in the literature. Effects of different parameters such as vibration amplitude, boundary conditions, material inhomogenity, electrical and thermal loading on the nonlinear behavior of PFG beams are presented.

scholarly journals Research on the Buckling Behavior of Functionally Graded Plates with Stiffeners Based on the Third-Order Shear Deformation Theory

Materials ◽  
2019 ◽  
Vol 12 (8) ◽  
pp. 1262 ◽  
Author(s):  
Hoang-Nam Nguyen ◽  
Tran Cong Tan ◽  
Doan Trac Luat ◽  
Van-Duc Phan ◽  
Do Van Thom ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
High Strength ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Width Ratio ◽  
Element Formulation ◽  
Power Law Distribution ◽  
Third Order

This paper presents a finite element formulation to study the mechanical buckling of stiffened functionally graded material (FGM) plates. The approach is based on a third-order shear deformation theory (TSDT) introduced by Guangyu Shi. The material properties of the plate were assumed to be varied in the thickness direction by a power law distribution, but the material of the stiffener was the same as that of the one of the bottom surface where the stiffener was placed. A parametric study was carried out to highlight the effect of material distribution, the thickness-to-width ratio, and stiffener parameters on the buckling characteristics of the stiffened FGM plates. Numerical results showed that the addition of stiffener to the FGM plate could significantly reduce the weight of the FGM plate but that both the FGM plates with and without stiffener had equally high strength in the same boundary condition and compression loading.

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