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 Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 1: Governing equations

2017 ◽  
Vol 39 (3) ◽  
pp. 245-257
Author(s):  
Dang Thuy Dong ◽  
Dao Van Dung
Keyword(s):  
Nonlinear Vibration ◽  
Thermal Loading ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Nonlinear Frequency ◽  
Governing Equations ◽  
Shallow Shells ◽  
Geometrical Imperfection ◽  
Graded Material ◽  
Doubly Curved

Nonlinear vibration of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners subjected to mechanical and thermal loading are investigated based on the first-order shear deformation theory (FSDT) with von Karman type nonlinearity, taking into account initial geometrical imperfection and smeared stiffener technique. Four material models of the FGM sandwich shells are presented. Explicit expressions for natural frequencies, nonlinear frequency-amplitude relation, and time-deflection curves of the FGM sandwich shallow shells are derived using Galerkin method.

A third-order shear deformation theory for nonlinear vibration analysis of stiffened functionally graded material sandwich doubly curved shallow shells with four material models

2017 ◽  
Vol 21 (4) ◽  
pp. 1316-1356 ◽  
Author(s):  
Dang T Dong ◽  
Dao Van Dung
Keyword(s):  
Functionally Graded Material ◽  
Vibration Analysis ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Third Order ◽  
Shallow Shells ◽  
Graded Material ◽  
Doubly Curved

This study presents a nonlinear vibration analysis of function graded sandwich doubly curved shallow shells, which reinforced by functionally graded material stiffeners and rested on the Pasternak foundation. The shells are subjected to the combination of mechanical, thermal, and damping loading. Four models of the sandwich shells with general sigmoid and power laws distribution are considered. The governing equations are established based on the third-order shear deformation theory. Von Kármán-type nonlinearity and smeared stiffener technique are taken into account. The explicit expressions for determining natural frequencies, nonlinear frequency–amplitude relation, and time–deflection curves are obtained by employing the Galerkin method. Finally, the fourth-order Runge–Kutta method is applied to investigate the influences of functionally graded material stiffeners, the boundary conditions, the models of the shells, thermal environment, foundation and geometrical parameters on the natural frequencies and dynamic nonlinear responses of the sandwich shells.

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

2018 ◽  
Vol 53 (6) ◽  
pp. 446-462 ◽  
Author(s):  
Amlan Paul ◽  
Debabrata Das
Keyword(s):  
Frequency Response ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Loading ◽  
Thermal Environment ◽  
Harmonic Excitation ◽  
Functionally Graded ◽  
Non Linear ◽  
Graded Material ◽  
Shear Deformable

Geometrically non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam under harmonic excitation and supported on three-parameter non-linear elastic foundation is presented. The beam is immovably clamped and is considered to be under static thermal loading due to uniform temperature rise. Reddy’s third-order shear-deformable beam theory in conjunction with von Kármán geometric non-linearity is considered to derive the governing equations employing Hamilton’s principle, and Ritz method is followed for approximating the displacement and rotation fields. A numerical algorithm based on iterative substitution method and Broyden’s method is proposed to predict the stable regions of frequency-response behavior. The frequency-response curves are presented in normalized plane for variations of load-amplitude, elastic foundation parameters, temperature rise, gradation index and functionally graded material composition, and their effects are discussed in detail. It is found that the load-amplitude, elastic foundation parameters, thermal loading and some of the functionally graded material compositions significantly affect the frequency response; whereas, the effect of gradation index is found to be relatively small. A comparative frequency-response curve between Voigt model and Mori–Tanaka scheme of functionally graded material modeling is presented, and it shows negligible difference between these two models. The present problem under thermal environment is studied for the first time through this work, and the proposed model and the numerical algorithm provide a simplified approach to study the non-linear frequency-response behavior.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

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.

Vibration of a Temperature-Dependent Thermally Pre/Postbuckled FGM Beam Over a Nonlinear Hardening Elastic Foundation

2013 ◽  
Vol 81 (1) ◽  
Author(s):  
S. E. Esfahani ◽  
Y. Kiani ◽  
M. Komijani ◽  
M. R. Eslami
Keyword(s):  
Elastic Foundation ◽  
Small Amplitude ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Temperature Dependent ◽  
Graded Material ◽  
Fgm Beam ◽  
Generalized Differential ◽  
Nonlinear Hardening ◽  
Raphson Method

Small amplitude vibrations of a functionally graded material beam under in-plane thermal loading in the prebuckling and postbuckling regimes is studied in this paper. The material properties of the FGM media are considered as function of both position and temperature. A three parameters elastic foundation including the linear and nonlinear Winkler springs along with the Pasternak shear layer is in contact with beam in deformation, which acts in tension as well as in compression. The solution is sought in two regimes. The first one, a static phase with large amplitude response, and the second one, a dynamic regime near the static one with small amplitude. In both regimes, nonlinear governing equations are discretized using the generalized differential quadrature (GDQ) method and solved iteratively via the Newton–Raphson method. It is concluded that depending on the type of boundary condition and loading type, free vibration of a beam under in-plane thermal loading may reach zero at a certain temperature which indicates the existence of bifurcation type of instability.

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.

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