scholarly journals Structural Analysis of Functionally Graded Material Using Sigmioadal and Power Law

Diagnostyka ◽  
2021 ◽  
pp. 59-65
Author(s):  
Nabel Abd-Ali ◽  
Ahmed Madeh
Keyword(s):  
Structural Analysis ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Graded Material

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.

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

BI-STABLE ANALYSES OF LAMINATED FGM SHELLS

2012 ◽  
Vol 12 (02) ◽  
pp. 311-335 ◽  
Author(s):  
X. Q. HE ◽  
L. LI ◽  
S. KITIPORNCHAI ◽  
C. M. WANG ◽  
H. P. ZHU
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Optimum Combination ◽  
Thickness Direction ◽  
Power Law Distribution ◽  
Deployable Structures ◽  
Graded Material ◽  
Two Parameter

Based on an inextensional two-parameter analytical model for cylindrical shells, bi-stable analyses were carried out on laminated functionally graded material (FGM) shells with various layups of fibers. Properties of FGM shells are functionally graded in the thickness direction according to a volume fraction power law distribution. The effects of constituent volume fractions of FGM matrix are examined on the curvature and twist of laminated FGM shells. The results reveal that the optimum combination of constituents of FGM matrix can be obtained for the maximum twist of FGM shells with antisymmetric layups, which helps the design of deployable structures. The effects of Young's modulus of fibers and the symmetry of layups on bi-stable behaviors are also discussed in detail.

Nonlinear stability analysis of stiffened functionally graded material sandwich cylindrical shells with general Sigmoid law and power law in thermal environment using third-order shear deformation theory

2017 ◽  
Vol 21 (3) ◽  
pp. 938-972 ◽  
Author(s):  
Dao Van Dung ◽  
Nguyen Thi Nga ◽  
Pham Minh Vuong
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Nonlinear Stability ◽  
Functionally Graded Material ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Functionally Graded ◽  
Thermal Loads ◽  
Third Order ◽  
Graded Material

This paper investigates analytically nonlinear buckling and postbuckling of functionally graded sandwich circular thick cylindrical shells filled inside by Pasternak two-parameter elastic foundations under thermal loads and axial compression loads. Shells are reinforced by closely spaced functionally graded material (FGM) rings and stringers. The temperature field is taken into account. Two general Sigmoid law and general power law, with four models of stiffened FGM sandwich cylindrical shell, are proposed. Using the Reddy’s third-order shear deformation shell theory (TSDT), stress function, and Lekhnitsky’s smeared stiffeners technique, the governing equations are derived. The closed form to determine critical axial load and postbuckling load-deflection curves are obtained by the Galerkin method. The effects of the face sheet thickness to total thickness ratio, stiffener, foundation, material, and dimensional parameters on critical thermal loads, critical mechanical loads and postbuckling behavior of shells are analyzed. In addition, this paper shows that for thin shells we can use the classical shell theory to investigate stability behavior of shell, but for thicker shells the use of TSDT for analyzing nonlinear stability of shell is necessary and suitable.

scholarly journals ON THE MECHANICAL RESPONSE OF A PRESSURIZED FUNCTIONALLY-GRADED CYLINDER

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Vlado Lubarda
Keyword(s):  
Shear Stress ◽  
Power Law ◽  
Functionally Graded Material ◽  
Elastic Moduli ◽  
Mechanical Response ◽  
Maximum Shear Stress ◽  
Radial Distance ◽  
Functionally Graded ◽  
Graded Material ◽  
Radial Inhomogeneity

A pressurized functionally-graded cylinder is considered made of the material whose elastic moduli vary with the radial distance according to the power-law relation. Some peculiar features of the mechanical response are noted for an incompressible functionally-graded material with the power of radial inhomogeneity equal to two. In particular, it is shown that the maximum shear stress is constant throughout the cylinder, while the displacement changes proportional to 1/r along the radial distance. No displacement takes place at all under equal pressures applied at both boundaries.

Viscoelastic Functionally Graded Materials Subjected to Antiplane Shear Fracture

2000 ◽  
Vol 68 (2) ◽  
pp. 284-293 ◽  
Author(s):  
G. H. Paulino ◽  
Z.-H. Jin
Keyword(s):  
Relaxation Time ◽  
Stress Intensity ◽  
Power Law ◽  
Functionally Graded Material ◽  
Relaxation Function ◽  
Functionally Graded ◽  
Antiplane Shear ◽  
Intensity Factors ◽  
Graded Material ◽  
Shear Relaxation

In this paper, a crack in a strip of a viscoelastic functionally graded material is studied under antiplane shear conditions. The shear relaxation function of the material is assumed as μ=μ0 expβy/hft, where h is a length scale and f(t) is a nondimensional function of time t having either the form ft=μ∞/μ0+1−μ∞/μ0exp−t/t0 for a linear standard solid, or ft=t0/tq for a power-law material model. We also consider the shear relaxation function μ=μ0 expβy/h[t0 expδy/h/t]q in which the relaxation time depends on the Cartesian coordinate y exponentially. Thus this latter model represents a power-law material with position-dependent relaxation time. In the above expressions, the parameters β, μ0,μ∞,t0; δ, q are material constants. An elastic crack problem is first solved and the correspondence principle (revisited) is used to obtain stress intensity factors for the viscoelastic functionally graded material. Formulas for stress intensity factors and crack displacement profiles are derived. Results for these quantities are discussed considering various material models and loading conditions.

Buckling and free vibration analysis of functionally graded sandwich plates and shallow shells by the Ritz method and the R-functions theory

2020 ◽  
pp. 095440622093630
Author(s):  
LV Kurpa ◽  
TV Shmatko
Keyword(s):  
Power Law ◽  
Functionally Graded Material ◽  
Complex Shape ◽  
Ritz Method ◽  
Mathematical Formulation ◽  
Functionally Graded ◽  
Buckling Load ◽  
Shallow Shells ◽  
Graded Material ◽  
R Functions

The purpose of the paper is to study stability and free vibrations of laminated plates and shallow shells composed of functionally graded materials. The approach proposed incorporates the Ritz method and the R-functions theory. It is assumed that the shell consists of three layers and is loaded in the middle plane. The both cases of uniform as well as non-uniform load are possible. The power-law distribution in terms of volume fractions is applied to get effective material properties for the layers. These properties are calculated for different arrangements and thicknesses of the layers by the analytical formulae obtained in the paper. The mathematical formulation is carried out in framework of the first-order shear deformation theory. The proposed approach consists of two steps. The first step is to define the pre-buckling state by solving the respective elasticity problem. The critical buckling load and frequencies of functionally graded material shallow shells are determined in the second step. The highlight of the method proposed is that it can be used for vibration and buckling analysis of plates and shallow shells of complex shape. The numerical results for frequencies and buckling load of plates and shallow shells of complex shape and different curvatures are presented to demonstrate the potential of the method developed. Different functionally graded material plates and shallow shells composed of a mixture of metal and ceramics are studied. The effects of the power law index, boundary conditions, thickness of the core, and face sheet layers on the fundamental frequencies and critical loads are discussed in this paper. The main advantage of the method is that it provides an analytical representation of the unknown solution, which is important when solving nonlinear problems.

scholarly journals Asymmetric bifurcation of thermally and electrically actuated functionally graded material microbeam

2016 ◽  
Vol 472 (2186) ◽  
pp. 20150597 ◽  
Author(s):  
X. Chen ◽  
S. A. Meguid
Keyword(s):  
Temperature Field ◽  
Symmetry Breaking ◽  
Power Law ◽  
Functionally Graded Material ◽  
Electrostatic Force ◽  
Functionally Graded ◽  
Beam Model ◽  
Uniform Temperature ◽  
Graded Material ◽  
Uniform Temperature Field

In this paper, we investigate the symmetric snap-through buckling and the asymmetric bifurcation behaviours of an initially curved functionally graded material (FGM) microbeam subject to the electrostatic force and uniform/non-uniform temperature field. The beam model is developed in the framework of Euler–Bernoulli beam theory, accounting for the through-thickness power law variation of the beam material and the physical neutral plane. Based on the Galerkin decomposition method, the beam model is simplified as a 2 d.f. reduced-order model, from which the necessary snap-through and symmetry breaking criteria are derived. The results of our work reveal the significant effects of the power law index on the snap-through and symmetry breaking criteria. Our results also reveal that the non-uniform temperature field can actuate the FGM microbeam and induce the snap-through and asymmetric bifurcation behaviours.

Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects

2020 ◽  
Vol 234 (18) ◽  
pp. 3667-3688
Author(s):  
Ismail Bensaid ◽  
Ahmed Amine Daikh ◽  
Ahmed Drai
Keyword(s):  
Free Vibration ◽  
Power Law ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Size Dependent ◽  
Graded Material

The investigation conducted in this paper aims to study free vibration and buckling behaviors of size-dependent functionally graded sandwich nanobeams. In order to take into account the small size effects, nonlocal elasticity theory of Eringen's is incorporated. Material properties of the functionally graded sandwich beams are supposed to change continuously through the thickness direction according to two forms of the volume fraction of constituents by power law functionally graded material and sigmoid law functionally graded material. These rules are modified to consider the effect of porosity, which covers four kinds of porosity distributions. Two types of sandwich nanobeams were provided: (a) homogeneous core and functionally graded skins and (b) functionally graded core and homogeneous skins. Third-order shear deformation theory without any shear correction factor in conjunction with Hamilton's principle is used to extract the governing equations of motions of porous functionally graded sandwich nanobeams and then solved analytically for two hinged ends. The effects of nonlocal parameter, length to thickness ratios, material graduation index, amount of porosity, porosity distribution shape, on the nondimensional frequency and critical buckling load of the functionally graded sandwich nanobeams made of porous materials are exhibited by a parametric study.

scholarly journals Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Woo-Young Jung ◽  
Sung-Cheon Han
Keyword(s):  
Elasticity Theory ◽  
Shear Deformation ◽  
Power Law ◽  
Functionally Graded Material ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Vibration Response ◽  
First Order ◽  
Graded Material

Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.

Sign in / Sign up

Export Citation Format

Share Document