A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation

Meccanica ◽  
2013 ◽  
Vol 49 (1) ◽  
pp. 91-109 ◽  
Author(s):  
V. Tahouneh ◽  
M. H. Naei
Keyword(s):  
Dynamic Analysis ◽  
Elastic Foundation ◽  
Power Law ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Two Parameter

Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials

2005 ◽  
Vol 72 (5) ◽  
pp. 788-791 ◽  
Author(s):  
Isaac Elishakoff ◽  
Cristina Gentilini
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Dimensional Solution ◽  
Energy Principle ◽  
Graded Materials

A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.

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.

scholarly journals Three-Dimensional Vibration Analysis of a Functionally Graded Sandwich Rectangular Plate Resting on an Elastic Foundation Using a Semi-Analytical Method

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3401 ◽  
Author(s):  
Cui ◽  
Zhou ◽  
Ye ◽  
Gaidai ◽  
Li ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Elastic Foundation ◽  
Power Law ◽  
Analytical Method ◽  
Sandwich Plate ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates

The three-dimensional vibration of a functionally graded sandwich rectangular plate on an elastic foundation with normal boundary conditions was analyzed using a semi-analytical method based on three-dimensional elasticity theory. The material properties of the sandwich plate varied with thickness according to the power law distribution. Two types of functionally graded material (FGM) sandwich plates were investigated in this paper: one with a homogeneous core and FGM facesheets, and another with homogeneous panels and an FGM core. Various displacements of the plates were created using an improved Fourier series consisting of a standard Fourier cosine series along with a certain number of closed-form auxiliary functions satisfying the essential boundary conditions. The vibration behavior of the FGM sandwich plate, including the natural frequencies and mode shapes, was obtained using the Ritz method. The effectiveness and accuracy of the suggested technique were fully verified by comparing the natural frequencies of sandwich plates with results from investigations of other functionally graded sandwich rectangular plates in the literature. A parametric study, including elastic parameters, foundation parameters, power law exponents, and layer thickness ratios, was performed, and some new results are presented.

FREE VIBRATION OF FUNCTIONALLY GRADED THIN RECTANGULAR PLATES RESTING ON WINKLER ELASTIC FOUNDATION WITH GENERAL BOUNDARY CONDITIONS USING RAYLEIGH–RITZ METHOD

2014 ◽  
Vol 06 (04) ◽  
pp. 1450043 ◽  
Author(s):  
S. CHAKRAVERTY ◽  
K. K. PRADHAN
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Power Law ◽  
Ritz Method ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Aspect Ratios ◽  
Winkler Elastic Foundation ◽  
Special Cases

In this paper, free vibration of functionally graded (FG) rectangular plates subject to different sets of boundary conditions within the framework of classical plate theory is investigated. Rayleigh–Ritz method is used to obtain the generalized eigenvalue problem. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any sets of boundary conditions. Material properties of the FG plate are assumed to vary continuously in the thickness direction of the constituents according to power-law form. The objective is to study the effects of constituent volume fractions, aspect ratios and power-law indices on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. Comparison with the results from the existing literature are provided for validation in special cases. Three-dimensional mode shapes are presented for FG square plates having various boundary conditions at the edges for different power-law indices. The present investigation also involves the rectangular FG plate to lay on a uniform Winkler elastic foundation. New results for the eigenfrequencies associated with foundation parameters are also reported here with the validation in special cases after checking a convergence pattern.

Free Vibration Analysis of Functionally Graded Plates on Two-Parameter Elastic Supports and in Contact With Stationary Fluid

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Arash Shahbaztabar ◽  
Ahmad Rahbar Ranji
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Volume Fraction ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Fg Plates ◽  
The Impact ◽  
Two Parameter

Free vibration analysis of functionally graded (FG) rectangular plates on two-parameter elastic foundation and vertically coupled with fluid is the objective of this work. The fluid domain is considered to be infinite in length, but it is bounded in depth and width directions, and the effects of hydrostatic pressure and free surface waves are not taken into account. The mechanical properties of the FG plates are assumed to vary continuously through the thickness direction according to a power-law distribution of the volume fraction of the constituents. The accuracy and applicability of the formulation is illustrated by comparison studies with those reported in the open literature. At the end, parametric studies are carried out to examine the impact of different parameters on the natural frequencies.

Dynamic analysis of functionally graded piezoelectric cylindrical panels by a three-dimensional mesh-free model

2017 ◽  
Vol 28 (18) ◽  
pp. 2516-2527 ◽  
Author(s):  
Mehrdad Foroutan ◽  
Farah Mohammadi ◽  
Jaber Alihemati ◽  
Arman Soltanimaleki
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Power Law Distribution ◽  
Mesh Free ◽  
Free Model ◽  
Cylindrical Panels ◽  
Functionally Graded Piezoelectric

In this work, dynamic analysis of functionally graded piezoelectric cylindrical panels is carried out under different mechanical and electrical loads and boundary conditions by a three-dimensional mesh-free model. Moving least squares approximation is used in the weak form of governing equations including three-dimensional equations of motion and Maxwell’s equation. Transformation method is applied to impose the essential boundary conditions. A power-law distribution is used to determine the effective material properties in the panel. The resulting system of differential equations is solved using Newmark time integration method. After validation of the proposed model, parametric study is carried out to investigate the effects of boundary conditions, geometry of panel, and distribution of constituent materials on natural frequencies and dynamic response of functionally graded piezoelectric panel.

Three-dimensional static analysis of thick functionally graded plates using graded finite element method

2013 ◽  
Vol 228 (8) ◽  
pp. 1275-1285 ◽  
Author(s):  
Hassan Zafarmand ◽  
Mehran Kadkhodayan
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Power Law ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Published Data ◽  
Power Law Distribution ◽  
Various Boundary Conditions ◽  
Graded Finite Element Method ◽  
Element Method

In this paper, a thick functionally graded plate based on three-dimensional equations of elasticity and subjected to nonuniform transverse loading is considered. The Young’s modulus of the plate is assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents and the Poisson’s ratio is assumed to be constant. Three-dimensional graded finite element method based on Rayleigh–Ritz energy formulation has been applied to study the static response of the plate. The plate deflection and in-plane stress for different values of the power law exponent, thickness-to-length ratio, and various boundary conditions have been investigated. To verify the presented method and data, the results are compared to published data.

scholarly journals Three-Dimensional Buckling Analysis of Functionally Graded Saturated Porous Rectangular Plates under Combined Loading Conditions

2021 ◽  
Vol 11 (21) ◽  
pp. 10434
Author(s):  
Faraz Kiarasi ◽  
Masoud Babaei ◽  
Kamran Asemi ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Three Dimensional ◽  
Functionally Graded ◽  
Constitutive Law ◽  
Combined Loading ◽  
Rectangular Plates ◽  
Loading Conditions ◽  
Classical Elasticity ◽  
Novel Approach ◽  
Buckling Behavior ◽  
Generalized Differential

The present work studies the buckling behavior of functionally graded (FG) porous rectangular plates subjected to different loading conditions. Three different porosity distributions are assumed throughout the thickness, namely, a nonlinear symmetric, a nonlinear asymmetric and a uniform distribution. A novel approach is proposed here based on a combination of the generalized differential quadrature (GDQ) method and finite elements (FEs), labeled here as the FE-GDQ method, while assuming a Biot’s constitutive law in lieu of the classical elasticity relations. A parametric study is performed systematically to study the sensitivity of the buckling response of porous structures, to different input parameters, such as the aspect ratio, porosity and Skempton coefficients, along with different boundary conditions (BCs) and porosity distributions, with promising and useful conclusions for design purposes of many engineering structural porous members.

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