A quasi-three-dimensional isogeometric model for porous sandwich functionally graded plates reinforced with graphene nanoplatelets

2021 ◽  
pp. 109963622110204
Author(s):  
Nam V Nguyen ◽  
H Nguyen-Xuan ◽  
Jaehong Lee
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Core Layer ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Plate Structures ◽  
Graded Materials ◽  
Fg Plates

The purpose of this study is to present a quasi-three-dimensional (quasi-3D) shear deformation theory for static bending and free vibration analyses of porous sandwich functionally graded (FG) plates with graphene nanoplatelets (GPLs) reinforcement. In addition, we propose a novel sandwich plate model with various outstanding features in terms of structural performance. The quasi-3D theory-based isogeometric analysis (IGA) in conjunction with refined plate theory (RPT) is first exploited to capture adequately the thickness stretching effect for porous sandwich FG plate structures reinforced with GPLs. The Non-Uniform Rational B-Splines (NURBS)-based IGA is employed in order to describe exactly the geometry models as well as approximate the unknown field with higher-order derivatives and continuity requirements while the RPT model includes only four essential variables. The sandwich FG plates consist of a core layer containing internal pores reinforced by GPLs and two functionally graded materials (FGMs) skin layers. Effective mechanical properties can be evaluated by employing the Halpin-Tsai model along with the rule of mixture. Various combinations of two porosity distributions and three GPL dispersions in the core layer are thoroughly investigated. Several numerical investigations are conducted to examine the effects of several key parameters on the static bending and free vibration behaviors of sandwich FG plate structures.

scholarly journals Three-Dimensional Finite Element Modeling of Thermomechanical Problems in Functionally Graded Hydroxyapatite/Titanium Plate

2014 ◽  
Vol 2014 ◽  
pp. 1-20 ◽  
Author(s):  
S. N. S. Jamaludin ◽  
S. Basri ◽  
Ahmad Hussain ◽  
Dheya Shujaa Al-Othmany ◽  
F. Mustapha ◽  
...  
Keyword(s):  
Thermal Stresses ◽  
Three Dimensional ◽  
Metallic Phase ◽  
Functionally Graded ◽  
Thermomechanical Model ◽  
Graded Materials ◽  
Ceramic Phase ◽  
Fg Plates ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

The composition of hydroxyapatite (HA) as the ceramic phase and titanium (Ti) as the metallic phase in HA/Ti functionally graded materials (FGMs) shows an excellent combination of high biocompatibility and high mechanical properties in a structure. Because the gradation of these properties is one of the factors that affects the response of the functionally graded (FG) plates, this paper is presented to show the domination of the grading parameter on the displacement and stress distribution of the plates. A three-dimensional (3D) thermomechanical model of a 20-node brick quadratic element is used in the simulation of the thermoelastic behaviors of HA/Ti FG plates subjected to constant and functional thermal, mechanical, and thermomechanical loadings. The convergence properties of the present results are examined thoroughly in order to assess the accuracy of the theory applied and to compare them with the established research results. Instead of the grading parameter, this study reveals that the loading field distribution can be another factor that reflects the thermoelastic properties of the HA/Ti FG plates. The FG structure is found to be able to withstand the thermal stresses while preserving the high toughness properties and thus shows its ability to operate at high temperature.

Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities

2019 ◽  
Vol 25 ◽  
pp. 69-83 ◽  
Author(s):  
Slimane Merdaci
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Vibration Analysis ◽  
Equations Of Motion ◽  
Porous Plate ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Fg Plates

This article presents the free vibration analysis of simply supported plate FG porous using a high order shear deformation theory. In is work the material properties of the porous plate FG vary across the thickness. The proposed theory contains four unknowns unlike the other theories which contain five unknowns. This theory has a parabolic shear deformation distribution across the thickness. So it is useless to use the shear correction factors. The Hamilton's principle will be used herein to determine the equations of motion. Since, the plate are simply supported the Navier procedure will be retained. To show the precision of this model, several comparisons have been made between the present results and those of existing theories in the literature for non-porous plates. Effects of the exponent graded and porosity factors are investigated.

High-order free vibration analysis of FGM sandwich plates with non-monotonically graded flexible core

2016 ◽  
Vol 20 (6) ◽  
pp. 759-780 ◽  
Author(s):  
Ming Liu ◽  
Jun Liu ◽  
Yuansheng Cheng
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Core Layer ◽  
Functionally Graded ◽  
High Order ◽  
Sandwich Plates ◽  
The Face ◽  
Flexible Core

Free vibration analysis of sandwich plates with non-monotonically graded flexible core is studied using a high-order sandwich panel theory. The non-monotonically graded flexible core is considered as two monotonically graded flexible core layers. In this high-order theory, the first-order shear deformation theory is used for the face sheets and a 3D-elasticity solution of weak core is employed for each single core layer. The laminated two-layered core is analyzed and formulated by the mixed layer-wise theory. Based on the continuity of the displacements and transverse stresses at the interfaces of the face sheets and the core, equations of motion are derived by Hamilton’s principle. The accuracy of the present approach is validated by comparing with the numerical results obtained from finite element method and good agreements are reached. Parametric study is also conducted to investigate the effect of distribution of functionally graded material properties, the monotonically graded core thickness ratio, and the thickness-to-side ratio on the vibration frequency.

3-D Free Vibration Analysis of Functionally Graded Thick Circular and Annular Plates on Elastic Foundation

2010 ◽  
Author(s):  
Vahid Tajeddini ◽  
Abdolreza Ohadi ◽  
Mojtaba Sadighi
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Small Strain ◽  
Functionally Graded ◽  
Different Boundary Conditions ◽  
Fg Plates

This paper describes a study of three-dimensional free vibration analysis of thick circular and annular functionally graded (FG) plates resting on Pasternak foundation. The formulation is based on the linear, small strain and exact elasticity theory. Plates with different boundary conditions are considered and the material properties of the FG plate are assumed to vary continuously through the thickness according to power law. The kinematic and the potential energy of the plate-foundation system are formulated and the polynomial-Ritz method is used to solve the eigenvalue problem. Convergence and comparison studies are done to demonstrate the correctness and accuracy of the present method. With respect to geometric parameters, elastic coefficients of foundation and different boundary conditions some new results are reported which maybe used as a benchmark solution for future researches.

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.

scholarly journals Coupled Free Vibration of Spinning Functionally Graded Porous Double-Bladed Disk Systems Reinforced with Graphene Nanoplatelets

Materials ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 5610
Author(s):  
Tianyu Zhao ◽  
Yu Ma ◽  
Hongyuan Zhang ◽  
Jie Yang
Keyword(s):  
Free Vibration ◽  
Distribution Pattern ◽  
Plate Theory ◽  
Synthesis Method ◽  
Coupled Model ◽  
Graphene Nanoplatelets ◽  
Functionally Graded ◽  
Width Ratio ◽  
Disk System ◽  
Bladed Disk

This paper presents, for the first time, the mechanical model and theoretical analysis of free vibration of a spinning functionally graded graphene nanoplatelets reinforced composite (FG-GPLRC) porous double-bladed disk system. The nanocomposite rotor is made of porous metal matrix and graphene nanoplatelet (GPL) reinforcement material with different porosity and nanofillers distributions. The effective material properties of the system are graded in a layer-wise manner along the thickness directions of the blade and disk. Considering the gyroscopic effect, the coupled model of the double-bladed disk system is established based on Euler–Bernoulli beam theory for the blade and Kirchhoff’s plate theory for the disk. The governing equations of motion are derived by employing the Lagrange’s equation and then solved by employing the substructure mode synthesis method and the assumed modes method. A comprehensive parametric analysis is conducted to examine the effects of the distribution pattern, weight fraction, length-to-thickness ratio, and length-to-width ratio of graphene nanoplatelets, porosity distribution pattern, porosity coefficient, spinning speed, blade length, and disk inner radius on the free vibration characteristics of the FG-GPLRC double-bladed disk system.

scholarly journals An exponential-trigonometric higher order shear deformation theory (HSDT) for bending, free vibration, and buckling analysis of functionally graded materials (FGMs) plates

2020 ◽  
Vol 29 ◽  
pp. 096369351987573 ◽  
Author(s):  
Yamna Belkhodja ◽  
Djamel Ouinas ◽  
Fatima Zohra Zaoui ◽  
Hamida Fekirini
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Functionally Graded Materials ◽  
Transverse Shear ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Graded Materials

Two assumptions have been made based on by this proposed theory, which come from recently developed exponential–trigonometric shape function for transverse shear deformation effect and a simple higher order shear deformation theory for plate, based on a constraint between two rotational displacements of axis parallel to the plate midplane, about the axes x, y Cartesian coordinates system, which caused fewer unknown number. For the application of this method, a displacement field extended as only bending membrane for transverse displacement is used, a governing equations of motion as a result are determined according to Hamilton’s principle, and simplified using Navier analytical solutions, as well as the transverse shear stresses effect that satisfied the stress-free boundary conditions on the simply supported plate free faces as a parabolic variation along the thickness are taken into account. A functionally graded materials plates are chosen for the parametric study, where the plates are functionally graded continuously in materials through the plate thickness as a function of power law or exponential form. The aim of this study is to analyze the bending, free vibration as well as the buckling mechanical behaviors, where the results are more focused on the investigation of different parameters such as the volume fraction index, geometric ratios, frequency modes, in-plane compressive load parameters and material properties effects on the deflection, stresses, natural frequencies, and critical buckling load, which are validated in terms of accuracy and efficiency with other plate theories results found in the literature.

Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

2019 ◽  
Vol 19 (11) ◽  
pp. 1950136
Author(s):  
Mounia Khetib ◽  
Hichem Abbad ◽  
Nourredine Elmeiche ◽  
Ismail Mechab
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Refined Plate Theory ◽  
Various Boundary Conditions ◽  
Graded Material ◽  
Principle Of Virtual Displacements ◽  
Good Agreement

This paper presents a two-variable refined plate theory for free vibration of functionally graded material (FGM) plates lying on viscoelastic Winkler–Pasternak foundations. The present work aims to examine the vibrations by a higher-order shear deformation theory including a new function of warping. The governing equations are derived from the principle of virtual displacements. Some illustrative examples are given in an attempt to solve the free vibration problem of a rectangular plate with various boundary conditions. The effects of damping on free vibrations, considering various parameters, are examined in detail. In the end, it is concluded that the present results with the new shear shape function of viscoelastic foundation are found to be in good agreement with other available results and the proposed method can easily be used to solve free vibration problems of the FGM plates.

Exact 3-D Stress and Stiffness Analysis of Functionally Graded Sandwich Plates Using Sampling Surfaces Method

2014 ◽  
Author(s):  
Mehdi Darabi ◽  
Rajamohan Ganesan
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Three Dimensional ◽  
Core Layer ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Stress Distributions ◽  
Power Law Distribution ◽  
Approach Zero ◽  
Comparison Of The Results

In the present work, the three-dimensional analysis for the deflection and stress distributions of functionally graded ceramic–metal sandwich plates is developed based on the method of sampling surfaces (SaS). In accordance with this method, into each layer of the plate, reference surfaces that are not equally spaced and are parallel to the mid-surface of the plate are introduced, and the displacement vectors of these surfaces are chosen as unknown functions. Such a choice allows the representation of the governing equations of the proposed higher order layer-wise plate theory in a very compact form and also permits the derivation of strain–displacement relationships correctly describing all motions including the rigid-body motions of the functionally graded plate. Hence the 3D elasticity problem of the thick plate is efficiently solved. The material properties of sandwich plate’s face layer are assumed to be that of a two-constituent material that vary continuously through the thickness of the face sheet according to a power law distribution of the volume fraction of the constituents. The core layer is homogeneous and made of an isotropic ceramic material. The effects of the volume fraction of the material constituents and their distribution on the deflections and, in particular, the 3-D stress distributions as well as the effects of the length-to-width and length-to-thickness ratios of the plate are investigated. Comparison of the results of the present work with the results available in existing literature is carried out for a benchmark problem. It is shown that considering large number of SaS, which are located at interfaces and Chebyshev polynomial nodes, the accuracy of the solutions can be improved significantly wherein the error will approach zero value as the total number of surfaces in each layer become very large.

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