scholarly journals Formulation of a New Mixed Four-Node Quadrilateral Element for Static Bending Analysis of Variable Thickness Functionally Graded Material Plates

2021 ◽  
Vol 2021 ◽  
pp. 1-23
Author(s):  
Pham Van Vinh
Keyword(s):  
Functionally Graded Material ◽  
Variable Thickness ◽  
Mixed Finite Element ◽  
Plate Thickness ◽  
Functionally Graded ◽  
Thin Plates ◽  
Quadrilateral Element ◽  
Graded Material ◽  
Element Technique ◽  
Power Law Index

A new mixed four-node quadrilateral element (MiQ4) is established in this paper to investigate functionally graded material (FGM) plates with variable thickness. The proposed element is developed based on the first-order shear deformation and mixed finite element technique, so the new element does not need any selective or reduced numerical integration. Numerous basic tests have been carried out to demonstrate the accuracy and convergence of the proposed element. Besides, the numerical examples show that the present element is free of shear locking and is insensitive to the mesh distortion, especially for the case of very thin plates. The present element can be applied to analyze plates with arbitrary geometries; it leads to reducing the computation cost. Several parameter studies are performed to show the roles of some parameters such as the power-law index, side-to-thickness ratio, boundary conditions (BCs), and variation of the plate thickness on the static bending behavior of the FGM plates.

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.

Thermoelastic Transient Behavior for a Clamped FGM Circular Plate

2014 ◽  
Vol 14 (04) ◽  
pp. 1450005 ◽  
Author(s):  
Hong-Liang Dai ◽  
Xiang Yan ◽  
Lei Yang
Keyword(s):  
Circular Plate ◽  
Volume Fraction ◽  
Plate Thickness ◽  
Transient Behavior ◽  
Functionally Graded ◽  
Thin Plates ◽  
Power Law Distribution ◽  
Graded Material ◽  
Index Ratio ◽  
The Galerkin Method

In this paper, the thermoelastic transient behavior of a clamped circular plate composed of functionally graded material (FGM) is investigated. The material properties of the FGM circular plate are assumed to vary through the plate thickness according to a power law distribution of the volume fraction of constituent materials, except Poisson's ratio, which is assumed as constant. Based on the von Karman equation and classical theory of thin plates, the equation of motion for the FGM circular plate is derived by the Hamilton principle. The nonlinear governing equation is solved by the Galerkin method, along with Newmark's integration method, in an iterative manner. Numerical results reveal that the functional gradient index, ratio of thickness to radius, thermal and mechanical loads have significant effect on the thermoelastic transient behavior of the clamped FGM circular plate. The result presented herein may be used as a reference for solving other transient coupled problems of thermoelasticity.

Transient Response of Functionally Graded Material Circular Cylindrical Shells with Magnetostrictive Layer

2016 ◽  
Vol 32 (4) ◽  
pp. 473-478
Author(s):  
C.-C. Hong
Keyword(s):  
Transient Response ◽  
Functionally Graded Material ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Normal Displacement ◽  
Control Gain ◽  
Graded Material ◽  
Circular Cylindrical Shells ◽  
Generalized Differential ◽  
Power Law Index

AbstractThe generalized differential quadrature (GDQ) method is used to investigate the transient response of magnetostrictive functionally graded material (FGM) circular cylindrical shells. The effects of control gain value, thermal load temperature and power-law index on transient responses of dominant normal displacement and thermal stress are analyzed. With velocity feedback and suitable product values of coil constant by control gain in the magnetostrictive FGM shells can reduce the transient amplitude of displacement into a smaller value.

Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method

2007 ◽  
Vol 221 (11) ◽  
pp. 1241-1247 ◽  
Author(s):  
M H Naei ◽  
A Masoumi ◽  
A Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Simply Supported ◽  
Graded Material ◽  
Element Method

The current study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander's non-linear strain-displacement relation for thin plates. The finite-element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson's ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

Investigation on Application of Semiloof Shell Element for Isotropic, Composite and Functionally Graded Material

2018 ◽  
Vol 877 ◽  
pp. 372-377
Author(s):  
Kari Thangaratnam ◽  
Evangeline Kumar
Keyword(s):  
Functionally Graded Material ◽  
Material Properties ◽  
Volume Fraction ◽  
Shell Element ◽  
Functionally Graded ◽  
Thin Plates ◽  
Shell Elements ◽  
Isotropic Composite ◽  
Graded Material ◽  
Coarse Meshes

In this research article, semiloof shell element was used to study the behaviour of plate and shells under mechanical and thermal load for stress, free vibration, initially stressed vibration, mechanical buckling, and non-linear vibration. In the above cases, the material properties: Isotropic, Composite and Functionally Graded Material (FGM) were considered. Wherein, the material property for the FGM shells was assumed to vary through the thickness of the shell by varying the volume fraction of the constituent, whereas, for composites, classical laminated theory was used. Utilizing the semiloof shell element, and the above material properties, the package COMSAP was developed. From the obtained results, we have observed that with coarse meshes, semiloof shell elements present better results, and it is especially effective in the case of thin plates and shells.

Rapid Heating Induced Vibration of Magnetostrictive Functionally Graded Material Plates

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
C. C. Hong
Keyword(s):  
Functionally Graded Material ◽  
Dynamic Equilibrium ◽  
Rapid Heating ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material ◽  
Parametric Effects ◽  
Generalized Differential ◽  
Power Law Index ◽  
Layer Control

The thermal vibration study of magnetostrictive functionally graded material (FGM) plate under rapid heating is computed by using the generalized differential quadrature (GDQ) method. The dynamic equilibrium differential equations with displacements and shear rotations of magnetostrictive FGM plate under the rapid heating are normalized and discretized into the dynamic discretized equations. The computational solutions of magnetostrictive FGM plate with four simply supported edges are obtained. Some parametric effects on the magnetostrictive FGM plates are analyzed, they are: thickness of mounted magnetostrictive layer, control gains of the proportional negative derivative, rapid heating flux values, and power law index values of FGM plate.

Correspondence Relations Between Deflection, Buckling Load, and Frequencies of Thin Functionally Graded Material Plates and Those of Corresponding Homogeneous Plates

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Shi-Rong Li ◽  
Xuan Wang ◽  
Romesh C. Batra
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Thin Plates ◽  
Scaling Factors ◽  
Classical Plate Theory ◽  
Graded Material ◽  
Plane Membrane

Based on the classical plate theory (CPT), we derive scaling factors between solutions of bending, buckling and free vibration of isotropic functionally graded material (FGM) thin plates and those of the corresponding isotropic homogeneous plates. The effective material properties of the FGM plate are assumed to vary piecewise continuously in the thickness direction except for the Poisson ratio that is taken to be constant. The correspondence relations hold for plates of arbitrary geometry provided that the governing equations and boundary conditions are linear. When the stretching and bending stiffnesses of the FGM plate satisfy a relation, Poisson's ratio is constant and the boundary conditions are such that the in-plane membrane forces vanish, then there exists a physical neutral surface for the FGM plate that is usually different from the plate midsurface. Example problems studied verify the accuracy of scaling factors.

scholarly journals Three new hybrid quasi-3D and 2D higher-order shear deformation theories for free vibration analysis of functionally graded material monolayer and sandwich plates with stretching effect

2020 ◽  
Vol 29 ◽  
pp. 096369352094186
Author(s):  
Y Belkhodja ◽  
D Ouinas ◽  
H Fekirini ◽  
JA Viña Olay ◽  
M Touahmia
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Functionally Graded Material ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Graded Material

The present investigation brings to the readers three new hybrid higher-order shear deformation theory (HSDT) models and analyses the functionally graded material (FGM) plates. The major objective of this work is to develop three HSDTs in a unique formulation by polynomial–hyperbolic–exponential and polynomial–trigonometric forms, propose the three new HSDT models, investigate the effect of thickness stretching by considering a quasi-three-dimensional theory and analyse the free vibration of isotropic and FGM monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) plates to demonstrate the models ability. Therefore, the Hamilton’s principle is exploited to develop equations of motion based on a displacement field of only five unknowns, of which three of them distinguished the transverse displacement membranes through the plate thickness (bending, shear and stretching displacements). In addition, the analytical solutions are found by applying the Navier approach for a simply supported boundary conditions type. The theory also considered that transverse shear deformation effect satisfied the stress-free boundary conditions on the plate-free surfaces without any requirement of shear correction factors. The used mechanical properties followed the power law and the Mori–Tanaka scheme distributions through the plate thickness. The determined results explained the effects of different non-dimensional parameters, and the proposed HSDTs predict the proper responses for monolayer and sandwich (symmetric as well as non-symmetric, with hardcore as well as softcore) FGM plates in comparison with other different plates’ theories solutions found in the literature references, thus the reliability and accuracy of the present approach are ascertained. It is obtained that the present formulations of polynomial–hyperbolic–exponential and polynomial–trigonometric forms can be further extended to all existing HSDTs models, for numerous problems related to the shear deformable effect.

scholarly journals A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 404 ◽  
Author(s):  
Vu Nam ◽  
Pham Vinh ◽  
Nguyen Chinh ◽  
Do Thom ◽  
Tran Hong
Keyword(s):  
Mechanical Behavior ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
First Order ◽  
Graded Material ◽  
Fgm Beam

There are many beam models to simulate the variable thickness functionally graded material (FGM) beam, each model has advantages and disadvantages in computer aided engineering of the mechanical behavior of this beam. In this work, a new model of beam is presented to study the mechanical static bending, free vibration, and buckling behavior of the variable thickness functionally graded material beams. The formulations are based on modified first order shear deformation theory and interpolating polynomials. This new beam model is free of shear-locking for both thick and thin beams, is easy to apply in computation, and has efficiency in simulating the variable thickness beams. The effects of some parameters, such as the power-law material index, degree of non-uniformity index, and the length-to-height ratio, on the mechanical behavior of the variable thickness FGM beam are considered.

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