• Steel and Composite Structures
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• v.16 no.4
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Steel and Composite Structures
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• v.22 no.1
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• pp.161-182
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• 2016

A state space differential reproducing kernel (DRK) method is developed for the three-dimensional (3D) analysis of functionally graded material (FGM) axisymmetric circular plates with simply-supported and clamped edges. The strong formulation of this 3D elasticity axisymmetric problem is derived on the basis of the Reissner mixed variational theorem (RMVT), which consists of the Euler-Lagrange equations of this problem and its associated boundary conditions. The primary field variables are naturally independent of the circumferential coordinate, then interpolated in the radial coordinate using the early proposed DRK interpolation functions, and finally the state space equations of this problem are obtained, which represent a system of ordinary differential equations in the thickness coordinate. The state space DRK solutions can then be obtained by means of the transfer matrix method. The accuracy and convergence of this method are examined by comparing their solutions with the accurate ones available in the literature.

• Structural Engineering and Mechanics
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• v.60 no.2
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• pp.313-335
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• 2016

In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young's modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

• Steel and Composite Structures
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• v.44 no.2
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• pp.171-181
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• 2022

Functionally graded material (FGM) has been spotlighted as an advanced composite material due to its excellent thermo-mechanical performance. And the buckling of FGM resting on elastic foundations has been a challenging subject because its behavior is directly connected to the structural safety. In this context, this paper is concerned with a numerical buckling analysis of metal-ceramic FG plates resting on a two-parameter (Pasternak-type) elastic foundation. The buckling problem is formulated based on the neutral surface and the (1,1,0) hierarchical model, and it is numerically approximated by 2-D natural element method (NEM) which provides a high accuracy even for coarse grid. The derived eigenvalue equations are solved by employing Lanczos and Jacobi algorithms. The numerical results are compared with the reference solutions through the benchmark test, from which the reliability of present numerical method has been verified. Using the developed numerical method, the critical buckling loads of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.

• Structural Engineering and Mechanics
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• v.87 no.1
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• pp.29-46
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• 2023

Critical thermal buckling of functionally graded porous (FGP) sandwich plates under various types of thermal loading is considered. It is assumed that the mechanical and thermal nonhomogeneous properties of FGP sandwich plate vary smoothly by distribution of power law across the thickness of sandwich plate. In this paper, porosity defects are modeled as stiffness reduction criteria and included in the rule of mixture. The thermal environments are considered as uniform, linear and nonlinear temperature rises. The critical buckling temperature response of FGM sandwich plates has been analyzed under various boundary conditions. By comparing several numerical examples with the reference solutions, the results indicate that the present analysis has good accuracy and rapid convergence. Further, the effects of various parameters like distribution shape of porosity, sandwich combinations, aspect ratio, thickness ratio, boundary conditions on critical buckling temperature of FGP sandwich plate have been studied in this paper.

• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.299-312
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• 2018

In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metal-matrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elasto-plastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.

• Steel and Composite Structures
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• v.14 no.1
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• pp.85-104
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• 2013

The present work deals with the thermomechanical bending response of functionally graded plates resting on Winkler-Pasternak elastic foundations. Theoretical formulations are based on a recently developed refined trigonometric shear deformation theory (RTSDT). The theory accounts for trigonometric distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. Unlike the conventional trigonometric shear deformation theory, the present refined trigonometric shear deformation theory contains only four unknowns as against five in case of other shear deformation theories. The material properties of the functionally graded plates are assumed to vary continuously through the thickness, according to a simple power law distribution of the volume fraction of the constituents. The elastic foundation is modelled as two-parameter Pasternak foundation. The results of the shear deformation theories are compared together. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and elastic foundation parameters on the thermomechanical behavior of functionally graded plates. It can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical bending response of functionally graded plates.

• Steel and Composite Structures
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• v.20 no.1
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• pp.205-225
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• 2016

In this study the finite element method is utilized to predict the deflection and vibration characteristics of rectangular plates made of saturated porous functionally graded materials (PFGM) within the framework of the third order shear deformation plate theory. Material properties of PFGM plate are supposed to vary continuously along the thickness direction according to the power-law form and the porous plate is assumed of the form where pores are saturated with fluid. Various edge conditions of the plate are analyzed. The governing equations of motion are derived through energy method, using calculus of variations while the finite element model is derived based on the constitutive equation of the porous material. According to the numerical results, it is revealed that the proposed modeling and finite element approach can provide accurate deflection and frequency results of the PFGM plates as compared to the previously published results in literature. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as porosity volume fraction, material distribution profile, mode number and boundary conditions on the natural frequencies and deflection of the PFGM plates in detail. It is explicitly shown that the deflection and vibration behaviour of porous FGM plates are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FGM plates with porosity phases.

• Steel and Composite Structures
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• v.51 no.2
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• pp.185-202
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• 2024

In this research paper, and for the first time, wave propagations in sigmoidal imperfect functionally graded material plates are investigated using a simplified quasi-three-dimensionally higher shear deformation theory (Quasi-3D HSDTs). By employing an indeterminate integral for the transverse displacement in the shear components, the number of unknowns and governing equations in the current theory is reduced, thereby simplifying its application. Consequently, the present theories exhibit five fewer unknown variables compared to other Quasi-3D theories documented in the literature, eliminating the need for any correction coefficients as seen in the first shear deformation theory. The material properties of the functionally graded plates smoothly vary across the cross-section according to a sigmoid power law. The plates are considered imperfect, indicating a pore distribution throughout their thickness. The distribution of porosities is categorized into two types: even or uneven, with linear (L)-Type, exponential (E)-Type, logarithmic (Log)-Type, and Sinus (S)-Type distributions. The current quasi-3D shear deformation theories are applied to formulate governing equations for determining wave frequencies, and phase velocities are derived using Hamilton's principle. Dispersion relations are assumed as an analytical solution, and they are applied to obtain wave frequencies and phase velocities. A comprehensive parametric study is conducted to elucidate the influences of wavenumber, volume fraction, thickness ratio, and types of porosity distributions on wave propagation and phase velocities of the S-FGM plate. The findings of this investigation hold potential utility for studying and designing techniques for ultrasonic inspection and structural health monitoring.

• Earthquakes and Structures
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• v.16 no.5
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• pp.601-609
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• 2019

The effect of the porosity and its distribution shape on the normal and shear interfacial stresses of the FGM beam strengthened with FRP plate subjected to a uniformly distributed load are investigated analytically in the present paper. Basically, the governing equations of FGM beams with porosity strengthened with composite plates are identical to the ones without porosity. Nonetheless, when the effect of the porosity and its distribution shape are taken into account, the rule of mixture was reformulated to assess the material characteristics with the porosity phases and its distribution shape. This work discusses the influence of the gradient index, the porosity and its distribution shape on the interfacial stresses.