scholarly journals Bending analysis of functionally graded beam with porosities resting on elastic foundation based on neutral surface position

2019 ◽  
Vol 13 (1) ◽  
pp. 33-45 ◽  
Author(s):  
Nguyen Thi Bich Phuong ◽  
Tran Minh Tu ◽  
Hoang Thu Phuong ◽  
Nguyen Van Long
Keyword(s):  
Analytical Solution ◽  
Elastic Foundation ◽  
Power Law ◽  
Coupling Effect ◽  
Functionally Graded ◽  
Transverse Load ◽  
Neutral Surface ◽  
Equilibrium Equations ◽  
Functionally Graded Beam ◽  
Bending Analysis

In this paper, the Timoshenko beam theory is developed for bending analysis of functionally graded beams having porosities. Material properties are assumed to vary through the height of the beam according to a power law. Due to unsymmetrical material variation along the height of functionally graded beam, the neutral surface concept is proposed to remove the stretching and bending coupling effect to obtain an analytical solution. The equilibrium equations are derived using the principle of minimum total potential energy and the physical neutral surface concept. Navier-type analytical solution is obtained for functionally graded beam subjected to transverse load for simply supported boundary conditions. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. The influences of material parameters (porosity distributions, porosity coefficient, and power-law index), span-to-depth ratio and foundation parameter are investigated through numerical results. Keywords: functionally graded beam; bending analysis; porosity; elastic foundation; bending; neutral surface. Received 10 December 2018, Revised 28 December 2018, Accepted 24 January 2019

Analytical solution for bending analysis of functionally graded beam

2015 ◽  
Vol 19 (4) ◽  
pp. 829-841 ◽  
Author(s):  
Benoumrane Sallai ◽  
Lazreg Hadji ◽  
T. Hassaine Daouadji ◽  
E.A. Adda Bedia
Keyword(s):  
Analytical Solution ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Bending Analysis

Dynamic Stiffness Formulation for Out-of-Plane Natural Vibration of Elastically Supported Functionally Graded Plates

2021 ◽  
pp. 2150062
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Elastic Foundation ◽  
Power Law ◽  
Natural Vibration ◽  
Plate Theory ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Rotary Inertia ◽  
Neutral Surface ◽  
Edge Conditions ◽  
Elastically Supported

In this paper, the natural vibration characteristics of elastically supported functionally graded material plate are investigated using the dynamic stiffness method (DSM). Power-law functionally graded (P-FG) plate, the material properties of which vary smoothly along the thickness direction following the power-law function, that has been used for the analysis. Classical plate theory and Hamilton’s principle are used for deriving the governing differential equation of motion and associated edge conditions for P-FG plate supported by elastic foundation. During the formulation of dynamic stiffness (DS) matrix, the concepts of rotary inertia and neutral surface are implemented. Wittrick–Williams (W-W) algorithm is used as a solving technique for the DS matrix to compute eigenvalues. The results thus obtained by DSM for the isotropic, P-FG plate, and the P-FG plate with elastic foundation compare well with published results that are based on different analytical and numerical methods. The comparisons indicate that this approach is very accurate. Furthermore, results are provided for elastically supported P-FG plate under four different considerations in order to see the differences in frequencies with the inclusion or exclusion of neutral surface and/or rotary inertia. It is noticed that the inclusion of rotary inertia and neutral surface influences the eigenvalues of P-FG plate, and that cannot be discounted. The study also examines the influence of plate geometry, material gradient index, edge conditions, and elastic foundation modulus on the natural frequency of P-FG plate.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

Exact solution by dynamic stiffness method for the natural vibration of porous functionally graded plate considering neutral surface

2021 ◽  
pp. 146442072098817
Author(s):  
Md. Imran Ali ◽  
Mohammad Sikandar Azam
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Stiffness Matrix ◽  
Natural Vibration ◽  
Dynamic Stiffness ◽  
Functionally Graded ◽  
Neutral Surface ◽  
Functionally Graded Plate ◽  
Dynamic Stiffness Matrix ◽  
Graded Material

This paper presents the formulation of dynamic stiffness matrix for the natural vibration analysis of porous power-law functionally graded Levy-type plate. In the process of formulating the dynamic stiffness matrix, Kirchhoff-Love plate theory in tandem with the notion of neutral surface has been taken on board. The developed dynamic stiffness matrix, a transcendental function of frequency, has been solved through the Wittrick–Williams algorithm. Hamilton’s principle is used to obtain the equation of motion and associated natural boundary conditions of porous power-law functionally graded plate. The variation across the thickness of the functionally graded plate’s material properties follows the power-law function. During the fabrication process, the microvoids and pores develop in functionally graded material plates. Three types of porosity distributions are considered in this article: even, uneven, and logarithmic. The eigenvalues computed by the dynamic stiffness matrix using Wittrick–Williams algorithm for isotropic, power-law functionally graded, and porous power-law functionally graded plate are juxtaposed with previously referred results, and good agreement is found. The significance of various parameters of plate vis-à-vis aspect ratio ( L/b), boundary conditions, volume fraction index ( p), porosity parameter ( e), and porosity distribution on the eigenvalues of the porous power-law functionally graded plate is examined. The effect of material density ratio and Young’s modulus ratio on the natural vibration of porous power-law functionally graded plate is also explained in this article. The results also prove that the method provided in the present work is highly accurate and computationally efficient and could be confidently used as a reference for further study of porous functionally graded material plate.

scholarly journals Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function

2020 ◽  
Vol 10 (12) ◽  
pp. 4190
Author(s):  
Aleksandar Radaković ◽  
Dragan Čukanović ◽  
Gordana Bogdanović ◽  
Milan Blagojević ◽  
Blaža Stojanović ◽  
...  
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Power Law ◽  
Deformation Theory ◽  
Natural Frequencies ◽  
Shape Function ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
High Order ◽  
Functionally Graded Plate

Functionally graded square and rectangular plates of different thicknesses placed on the elastic foundation modeled according to the Winkler-Pasternak theory have been studied. The thermal and mechanical characteristics, apart from Poisson’s ratio, are considered to continuously differ through the thickness of the studied material as stated in a power-law distribution. A mathematical model of functionally graded plate which include interaction with elastic foundation is defined. The equilibrium and stability equations are derived using high order shear deformation theory that comprises various kinds of shape function and the von Karman nonlinearity. A new analytically integrable shape function has been introduced. Hamilton’s principle has been applied with the purpose of acquiring the equations of motion. An analytical method for identifying both natural frequencies and critical buckling temperature for cases of linear and nonlinear temperature change through the plate thickness has been established. In order to verify the derived theoretical results on numerical examples, an original program code has been implemented within software MATLAB. Critical buckling temperature and natural frequencies findings are shown below. Previous scientific research and papers confirms that presented both the theoretical formulation and the numerical results are accurate. The comparison has been made between newly established findings based on introduced shape function and the old findings that include 13 different shape functions available in previously published articles. The final part of the research provides analysis and conclusions related to the impact of the power-law index, foundation stiffness, and temperature gradient on critical buckling temperature and natural frequencies of the functionally graded plates.

scholarly journals Improved Stresses Analysis of a Functionally Graded Beam under Prestressed CFRP Plate

2018 ◽  
Vol 27 (1) ◽  
pp. 096369351802700 ◽  
Author(s):  
Samir Brairi ◽  
Bachir Kerboua ◽  
Ismail Bensaid
Keyword(s):  
Analytical Solution ◽  
Mechanical Load ◽  
Fe Analysis ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Interfacial Stresses ◽  
Geometrical Properties ◽  
Cfrp Plate ◽  
Practical Reality ◽  
New Research

In this paper, a new analytical solution is presented to predict the interfacial stresses of a functionally graded beam reinforced by a prestressed CFRP plate under thermo-mechanical load. A finite element (FE) analysis is also employed to validate the results of the analytical solution, the results from both models agreed very closely. Also, a parametric study is carried out in order to identify the effects of various material and geometrical properties on the magnitude of interfacial stresses. The presented results show that the interfacial stresses are highly concentrated at the end of the laminate, which can lead to a debonding at this location. Also, the material and geometrical properties have a significant impact on the magnitude of interfacial stresses. This new research approaches the practical reality of the structures in their environment by taking into consideration a combination of neglected terms by the other studies. Therefore, the results presented in this paper can serve as a benchmark for future analyses of functionally graded beams strengthened by prestressed Carbon fibre-rein-forced polymer (CFRP) plates and improve the rehabilitation, mechanical and corrosion resistance.

scholarly journals Improved Stresses Analysis of a Functionally Graded Beam under Prestressed CFRP Plate

2018 ◽  
Vol 27 (6) ◽  
pp. 096369351802700
Author(s):  
Samir Brairi ◽  
Bachir Kerboua ◽  
Ismail Bensaid
Keyword(s):  
Analytical Solution ◽  
Mechanical Load ◽  
Fe Analysis ◽  
Functionally Graded ◽  
Functionally Graded Beam ◽  
Interfacial Stresses ◽  
Geometrical Properties ◽  
Cfrp Plate ◽  
Practical Reality ◽  
New Research

In this paper, a new analytical solution is presented to predict the interfacial stresses of a functionally graded beam reinforced by a prestressed CFRP plate under thermo-mechanical load. A finite element (FE) analysis is also employed to validate the results of the analytical solution, the results from both models agreed very closely. Also, a parametric study is carried out in order to identify the effects of various material and geometrical properties on the magnitude of interfacial stresses. The presented results show that the interfacial stresses are highly concentrated at the end of the laminate, which can lead to a debonding at this location. Also, the material and geometrical properties have a significant impact on the magnitude of interfacial stresses. This new research approaches the practical reality of the structures in their environment by taking into consideration a combination of neglected terms by the other studies. Therefore, the results presented in this paper can serve as a benchmark for future analyses of functionally graded beams strengthened by prestressed Carbon fibre-rein-forced polymer (CFRP) plates and improve the rehabilitation, mechanical and corrosion resistance.

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