scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

Thermoelastic Stability of Imperfect Functionally Graded Plates Based on the Third Order Shear Deformation Theory

2006 ◽  
Author(s):  
B. Samsam Shariat ◽  
M. R. Eslami ◽  
A. Bagri
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Form Solution ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Equilibrium Equations ◽  
Third Order ◽  
The Third

Thermal buckling analysis of rectangular functionally graded plates with initial geometric imperfections is presented in this paper. It is assumed that the non-homogeneous mechanical properties vary linearly through the thickness of the plate. The plate is assumed to be under various types of thermal loadings, such as the uniform temperature rise and nonlinear temperature gradient through the thickness. A double-sine function for the geometric imperfection along the x and y-directions is considered. The equilibrium equations are derived using the third order shear deformation plate theory. Using a suitable method, equilibrium equations are reduced from 5 to 2 equations. The corresponding stability equations are established. Using these equations accompanied by the compatibility equation yield to the buckling loads in a closed form solution for each loading case. The results are compared with the known data in the literature.

A closed form solution for bending/stretching analysis of functionally graded circular plates under asymmetric loading using the Green function

2010 ◽  
Vol 224 (6) ◽  
pp. 1153-1163 ◽  
Author(s):  
A R Saidi ◽  
A Naderi ◽  
E Jomehzadeh
Keyword(s):  
Green Function ◽  
Closed Form ◽  
Volume Fraction ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Circular Plates ◽  
Equilibrium Equations

In this article, a closed-form solution for bending/stretching analysis of functionally graded (FG) circular plates under asymmetric loads is presented. It is assumed that the material properties of the FG plate are described by a power function of the thickness variable. The equilibrium equations are derived according to the classical plate theory using the principle of total potential energy. Two new functions are introduced to decouple the governing equilibrium equations. The three highly coupled partial differential equations are then converted into an independent equation in terms of transverse displacement. A closed-form solution for deflection of FG circular plates under arbitrary lateral eccentric concentrated force is obtained by defining a new coordinate system. This solution can be used as a Green function to obtain the closed-form solution of the FG plate under arbitrary loadings. Also, the solution is employed to solve some different asymmetric problems. Finally, the stress and displacement components are obtained exactly for each problem and the effect of volume fraction is also studied.

Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

2017 ◽  
Vol 34 (4) ◽  
pp. 1314-1331 ◽  
Author(s):  
W.X. Zhang ◽  
R.G. Liu ◽  
Y. Bai
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Graded Materials ◽  
Content Type ◽  
Displacement Constraints

Purpose For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs. Design/methodology/approach Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods. Findings In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints. Originality/value The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2193-2209
Author(s):  
Ehsan Ansari ◽  
AliReza Setoodeh
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Shear Deformation ◽  
Variable Thickness ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Predictions ◽  
Shear Deformation Plate Theory

This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

Nonlinear Thermo-Mechanical Vibration Analysis of Functionally Graded Beams

2011 ◽  
Author(s):  
Ali Fallah ◽  
Keikhosrow Firoozbakhsh ◽  
Abdolreza Pasharavesh
Keyword(s):  
Vibration Analysis ◽  
Vibration Amplitude ◽  
Thermal Loading ◽  
Natural Frequencies ◽  
Mechanical Vibration ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Form Solution ◽  
Functionally Graded ◽  
Material Inhomogeneity

In this paper, nonlinear thermo-mechanical free vibration analysis of functionally graded (FG) beams investigated. Euler-Bernoulli assumptions together with Von Karman’s strain-displacement relation are employed to derive the nonlinear governing partial differential equation (PDE) of motion. He’s variational method is employed to obtain a simple and efficient approximate closed form solution of the nonlinear governing equation. Comparison between results of the present work and those available in literature shows the accuracy of presented technique. Some new results for the nonlinear natural frequencies of the FG beams such as the effect of vibration amplitude, material inhomogeneity and thermal loading are presented for future references.

BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER MECHANICAL LOADING USING HIGHER ORDER FUNCTIONALLY GRADED STRIP

2013 ◽  
Vol 13 (06) ◽  
pp. 1350033 ◽  
Author(s):  
M. H. SHERAFAT ◽  
H. R. OVESY ◽  
S. A. M. GHANNADPOUR
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Load Capacity ◽  
Plate Thickness ◽  
Higher Order ◽  
Functionally Graded ◽  
Biaxial Compression ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Ceramic Phase

This paper is concerned with buckling analyses of rectangular functionally graded plates (FGPs) under uniaxial compression, biaxial compression and combined compression and tension loads. It is assumed that the plate is a mixture of metal and ceramic that its properties changes as afunction according to the simple power law distribution through the plate thickness. The fundamental eigen-buckling equations for rectangular plates of functionally graded material (FGM) are obtained by discretizing the plate into some finite strips, which are developed on the basis of the higher order plate theory (HOPT). The solution is obtained by the minimization of the total potential energy. Numerical results fora variety of FGPs are given, and compared with the available results, wherever possible. The effects of thickness ratio, variation of the volume fraction of the ceramic phase through the thickness, aspect ratio, boundary conditions and also load distribution on the buckling load capacity of FGM plates are determined and discussed. It is found that the buckling behavior of FGM plates is particularly influenced by application of HOPT, especially when the plates are thick.

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