• Advances in nano research
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• 제8권2호
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• pp.115-134
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• 2020

In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants and the aspect ratio with different boundary conditions on the free vibrations of nanoplates. To the best of the researchers' knowledge, in the literature, there is no study carried out into MSGT for free vibration analysis of FGM nanoplate with arbitrary functions.

• Steel and Composite Structures
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• 제18권4호
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• pp.1063-1081
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• 2015

In this paper, a new nonlocal hyperbolic refined plate model is presented for free vibration properties of functionally graded (FG) plates. This nonlocal nano-plate model incorporates the length scale parameter which can capture the small scale effect. The displacement field of the present theory is chosen based on a hyperbolic variation in the in-plane displacements through the thickness of the nano-plate. By dividing the transverse displacement into the bending and shear parts, the number of unknowns and equations of motion of the present theory is reduced, significantly facilitating structural analysis. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG nano-plate are computed using Mori-Tanaka homogenization scheme. The governing equations of motion are derived based on the nonlocal differential constitutive relations of Eringen in conjunction with the refined four variable plate theory via Hamilton's principle. Analytical solution for the simply supported FG nano-plates is obtained to verify the theory by comparing its results with other available solutions in the open literature. The effects of nonlocal parameter, the plate thickness, the plate aspect ratio, and various material compositions on the dynamic response of the FG nano-plate are discussed.

• Structural Engineering and Mechanics
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• 제84권6호
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• pp.813-822
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• 2022

In this article, the buckling and free vibration of multi-directional FGM sandwich plates are investigated. The material properties of FGM sandwich plates are assumed to be varying continuously in the in the longitudinal, transverse and thickness directions. The material properties are evaluated based on Voigt's micro-mechanical model considering power law distribution method with arbitrary power index. Equations of motion for the buckling and vibration analysis of multi-directional FGM sandwich plate are obtained based on refined shear deformation theory. Analytical solution for simply supported multidirectional FGM sandwich plate is carried out using Navier's solution technique. The FGM sandwich plate considered in this work has a homogeneous ceramic core and two functionally graded face sheets. Influence of volume fraction index in the longitudinal, transverse and thickness direction, layer thickness, and geometrical parameter over natural frequency and critical buckling load of multi-directional FGM sandwich plate is investigated. The finding shows a multi-directional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters have been identified which will guide researchers in selecting fabrication routes for improving the performance of such structures.

• Steel and Composite Structures
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• 제44권5호
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• pp.633-649
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• 2022

This paper is first implemented with the bending behavior of three-dimensional functionally graded (3DFG) plates in the framework of level set-based topology optimization (LS-based TO). Besides, due to the suitable properties of the current design domain, the thin-plate spline (TPS) is recognized as a RBF to construct the LS function. The overall mechanical properties of the 3DFG plate are assessed using a power-law distribution scheme via Mori-Tanaka micromechanical material model. The bending response is obtained using the first-order shear deformation theory (FSDT). The mixed interpolation of four elements of tensorial components (MITC4) is also implemented to overcome a well-known shear locking problem when the thickness becomes thinner. The Hamilton-Jacobi method is utilized in each iteration to enforce the necessary boundary conditions. The mathematical formulas are expressed in great detail for the LS-based TO using 3DFG materials. Several numerical examples are exhibited to verify the efficiency and reliability of the current methodology with the previously reported literature. Finally, the influences of FG materials in the optimized design are explained in detail to illustrate the behaviors of optimized structures.

• Steel and Composite Structures
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• 제20권1호
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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.

• Geomechanics and Engineering
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• 제12권1호
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• pp.9-34
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• 2017

In this work, an efficient and simple quasi-3D hyperbolic shear deformation theory is developed for bending and vibration analyses of functionally graded (FG) plates resting on two-parameter elastic foundation. The significant feature of this theory is that, in addition to including the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT). The foundation is described by the Pasternak (two-parameter) model. The material properties of the plate are assumed to vary continuously in the thickness direction by a simple power law distribution in terms of the volume fractions of the constituents. Equations of motion for thick FG plates are obtained within the Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The numerical results are given in detail and compared with the existing works such as 3-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates resting on elastic foundation.

• Structural Engineering and Mechanics
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• 제72권4호
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• pp.513-524
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• 2019

The present article deals with thermal buckling of functionally graded plates with porosity and resting on elastic foundation. The basic formulation is based on quasi 3D theory. The present theory contains only four unknowns and also accommodates the thickness stretching effect. Porosity-dependent material coefficients of the plate are compositionally graded throughout the thickness according to a modified micromechanical model. Different patterns of porosity distributions are considered. The thermal loads are assumed to be uniform, linear and non-linear temperature rises through the thickness direction. The plate is assumed to be simply supported on all edges. Various numerical examples are given to check the accuracy and reliability of the present solution, in which both the present results and those reported in the literature are provided. In addition, several numerous new results for thick FG plates with porosity are also presented.

• 국제강구조저널
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• 제18권4호
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• pp.1265-1283
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• 2018

This paper presents a four-variable first-order shear deformation theory considering in-plane rotation of functionally graded plates. In recent studies, a simple first-order shear deformation theory was developed and extended to functionally graded plates. It has only four variables, separating the deflection into bending and shear parts, while the conventional first-order shear deformation theory has five variables. However, this simple first-order shear deformation theory only provides good predictions for simply supported plates since it does not consider in-plane rotation varying through the thickness of the plates. The present theory also has four variables, but considers the variation of in-plane rotation such that it is able to correctly predict the responses of the plates with any boundary conditions. Analytical solutions are obtained for rectangular plates with various boundary conditions. Comparative studies demonstrate the effects of in-plane rotation and the accuracy of the present theory in predicting the responses of functionally graded plates.

• Structural Engineering and Mechanics
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• 제72권3호
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• pp.293-304
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• 2019

In this paper, a general model is developed to predict the distribution of interfacial shear and normal stresses of FG beam reinforced by porous FGM plates under mechanical loading. The beam is assumed to be isotropic with a constant Poisson's ratio and power law elastic modulus through the beam thickness. Stress distributions, depending on an inhomogeneity constant, were calculated and presented in graphicals forms. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam, and it is shown that the inhomogeneities play an important role in the distribution of interfacial stresses. The results presented in the paper can serve as a benchmark for future analyses of functionally graded beams strengthened by imperfect varying properties plates. Numerical comparisons between the existing solutions and the present new solution enable a clear appreciation of the effects of various parameters. The results of this study indicated that the imperfect functionally graded panel strengthening systems are effective in enhancing flexural behavior of the strengthened FGM beams. This research is helpful in understanding the mechanical behaviour of the interface and design of hybrid structures.

• Steel and Composite Structures
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• 제45권6호
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• pp.839-850
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• 2022

This paper presents an analytical solution to study the combined effect of non-local and stretching effect on the vibration of advanced functionally graded (FG) nanoplates. A new quasi-3D plate theory is presented; there are only five unknowns and any shear correction factor is used. A new displacement field with a new shear warping function is proposed. The equilibrium equations of the FG nanoplates are obtained using the Hamilton principle and solved numerically using the Navier technique. The material properties of functionally graded nanoplates are presumed to change according to the power-law distribution of ceramic and metal constituents. The numerical results of this work are compared with those of other published results to indicate the accuracy and convergence of this theory. Hence, a profound parameterstudy is also performed to show the influence of many parameters of the functionally graded nanoplates on the free vibration responses is investigated.