scholarly journals A Quasi-3D Higher-Order Theory for Bending of FG Nanoplates Embedded in an Elastic Medium in a Thermal Environment

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 234
Author(s):  
Ashraf M. Zenkour ◽  
Mashhour A. Alazwari ◽  
Ahmed F. Radwan
Keyword(s):  
Elastic Foundation ◽  
Thermal Environment ◽  
Nonlocal Elasticity Theory ◽  
Order Theory ◽  
Functionally Graded ◽  
Normal Strain ◽  
Shear Deformations ◽  
Higher Order Theory ◽  
Foundation Parameters ◽  
Transverse Normal Strain

This paper presents the effects of temperature and the nonlocal coefficient on the bending response of functionally graded (FG) nanoplates embedded in an elastic foundation in a thermal environment. The effects of transverse normal strain, as well as transverse shear strains, are considered where the variation of the material properties of the FG nanoplate are considered only in thickness direction. Unlike other shear and deformations theories in which the number of unknown functions is five and more, the present work uses shear and deformations theory with only four unknown functions. The four-unknown normal and shear deformations model, associated with Eringen nonlocal elasticity theory, is used to derive the equations of equilibrium utilizing the principle of virtual displacements. The effects due to nonlocal coefficient, side-to-thickness ratio, aspect ratio, normal and shear deformations, thermal load and elastic foundation parameters, as well as the gradation in FG nanoplate bending, are investigated. In addition, for validation, the results obtained from the present work are compared to ones available in the literature.

Nonlinear Vibration Analysis of Shear Deformable Functionally Graded Ceramic-Metal Plates Using an Improved Higher Order Theory

2010 ◽  
Author(s):  
Mohammad Talha ◽  
B. N. Singh
Keyword(s):  
Nonlinear Vibration ◽  
Vibration Analysis ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Higher Order Terms ◽  
Higher Order Theory ◽  
Shear Deformable

In the present study, an improved higher order theory in conjunction with finite element method (FEM) is presented and is applied to study the nonlinear vibration analysis of shear deformable functionally graded material (FGMs) plates. The present structural model kinematics assumes the cubically varying in-plane displacement over the entire thickness, while the transverse displacement varies quadratically to achieve the accountability of normal strain and its derivative in calculation of transverse shear strains. The theory also satisfies zero transverse strains conditions at the top and bottom faces of the plate, and the geometric nonlinearity is based on Green-Lagrange assumptions. All higher order terms appearing from nonlinear strain displacement relations are incorporated in the formulation. The material properties of the plates are assumed to vary smoothly and continuously throughout the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. A C0 continuous isoparametric nonlinear FEM with 13 degrees of freedom per node is proposed for the accomplishment of the improved elastic continuum. Numerical results with different system parameters and boundary conditions are accomplished, to show the importance and necessity of the higher order terms in the nonlinear formulations.

A refined sinusoidal model for functionally graded plates subjected to thermomechanical loading

2018 ◽  
Vol 53 (14) ◽  
pp. 1883-1896
Author(s):  
Ren Xiaohui ◽  
Wu Zhen
Keyword(s):  
Functionally Graded Material ◽  
Thermal Loading ◽  
Functionally Graded ◽  
Normal Strain ◽  
Sinusoidal Model ◽  
Proposed Model ◽  
Graded Material ◽  
Plane Displacement ◽  
Stress Free Boundary ◽  
Transverse Normal Strain

A refined sinusoidal model considering transverse normal strain has been developed for thermoelastic analysis of functionally graded material plate. Although transverse normal strain has been considered, the additional displacement parameters are not increased as transverse normal strain only includes the thermal expansion coefficient and thermal loading. Moreover, the merit of the previous sinusoidal model satisfying tangential stress-free boundary conditions on the surfaces can be maintained. It is important that the effects of transverse normal thermal deformation are incorporated in the in-plane displacement field, which can actively influence the accuracy of in-plane stresses. To assess the performance of the proposed model, the thermoelastic behaviors of functionally graded material plates with various configurations have been analyzed. Without increase of displacement variables, accuracy of the proposed model can be significantly improved by comparing to the previous sinusoidal model. Agreement between the present results and quasi-dimensional solutions are very good, and the proposed model only includes the five displacement variables which can illustrate the accuracy and effectiveness of the present model. In addition, new results using several models considered in this paper have been presented, which can serve as a reference for future investigations.

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 Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment

2019 ◽  
Vol 2019 ◽  
pp. 1-17 ◽  
Author(s):  
Zakaria Ibnorachid ◽  
Lhoucine Boutahar ◽  
Khalid EL Bikri ◽  
Rhali Benamar
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Slenderness Ratio ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement

In this paper, free vibrations of Porous Functionally Graded Beams (P-FGBs), resting on two-parameter elastic foundations, and exposed to three forms of thermal field, uniform, linear, and sinusoidal, are studied using a Refined Higher-order shear Deformation Theory. The present theory accounts for shear deformation by considering a constant transverse displacement and a higher-order variation of the axial displacement through the thickness of the beam. The stress-free boundary conditions are satisfied on the upper and lower surfaces of the beam without using any shear correction factor. The material properties are temperature-dependent and vary continuously through the depth direction of the beam, based on a modified power-law rule, in which two kinds of porosity distributions, uniform, and nonuniform, through the cross-section area of the beam, are considered. Hamilton’s principle is applied to obtain governing equations of motion, which are solved using a Navier-type analytical solution for simply supported P-FGB. Numerical examples are proposed and discussed in detail, to prove the effect of the thermal environment, the porosity distribution, and the influence of several parameters such as the power-law index, porosity volume fraction, slenderness ratio, and elastic foundation parameters on the critical buckling temperatures and the natural frequencies of the P-FGB.

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.

Linear Thermoelastic Higher-Order Theory for Periodic Multiphase Materials

2001 ◽  
Vol 68 (5) ◽  
pp. 697-707 ◽  
Author(s):  
J. Aboudi ◽  
M.-J. Pindera ◽  
S. M. Arnold
Keyword(s):  
Finite Element ◽  
Predictive Accuracy ◽  
Local Stress ◽  
Computer Code ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Infinite Matrix ◽  
Homogenization Technique ◽  
Higher Order Theory

A new micromechanics model is presented which is capable of accurately estimating both the effective elastic constants of a periodic multiphase composite and the local stress and strain fields in the individual phases. The model is presently limited to materials characterized by constituent phases that are continuous in one direction, but arbitrarily distributed within the repeating unit cell which characterizes the material’s periodic microstructure. The model’s analytical framework is based on the homogenization technique for periodic media, but the method of solution for the local displacement and stress fields borrows concepts previously employed by the authors in constructing the higher-order theory for functionally graded materials, in contrast with the standard finite element solution method typically used in conjunction with the homogenization technique. The present approach produces a closed-form macroscopic constitutive equation for a periodic multiphase material valid for both uniaxial and multiaxial loading which, in turn, can be incorporated into a structural analysis computer code. The model’s predictive accuracy is demonstrated by comparison with reported results of detailed finite element analyses of periodic composites as well as with the classical elasticity solution for an inclusion in an infinite matrix.

FREE VIBRATION OF FUNCTIONALLY GRADED ARBITRARY STRAIGHT-SIDED QUADRILATERAL PLATES RESTING ON ELASTIC FOUNDATIONS

2011 ◽  
Vol 03 (04) ◽  
pp. 825-843 ◽  
Author(s):  
A. ALIBEYGI BENI
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Shape ◽  
Computational Domain ◽  
Fg Plates

The free vibration of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation and in thermal environment is presented. The formulation is based on the first-order shear deformation theory (FSDT). The material properties are assumed to be temperature-dependent and graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then the discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic rectangular and FG rectangular and skew plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the frequency parameters of the FG plates are studied.

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