• Advances in aircraft and spacecraft science
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• v.7 no.2
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• pp.169-186
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• 2020

Based upon differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), mechanical-hygro-thermal vibrational analyzes of shear deformable porous functionally graded (FG) nanoplate on visco-elastic medium has been performed. The presented formulation incorporates two scale factors for examining vibrational behaviors of nano-dimension plates more accurately. The material properties for FG plate are porosity-dependent and defined employing a modified power-law form. It is supposed that the nano-size plate is exposed to hygro-thermal and variable compressive mechanical loadings. The governing equations achieved by Hamilton's principle are solved implementing DQM. Presented results indicate the prominence of moisture/temperature variation, damping factor, material gradient index, nonlocal coefficient, strain gradient coefficient and porosities on vibrational frequencies of FG nano-size plate.

• Smart Structures and Systems
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• v.21 no.4
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• pp.493-519
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• 2018

This article presents a finite element (FE) model to assess the free vibration and static response of a functionally graded skew magneto-electro-elastic (FGSMEE) plate. Through the thickness material grading of FGSMEE plate is achieved using power law distribution. The coupled constitutive equations along with the total potential energy approach are used to develop the FE model of FGSMEE plate. The transformation matrix is utilized in bringing out the element matrix corresponding to the global axis to a local axis along the skew edges to specify proper boundary conditions. The effect of skew angle on the natural frequency of an FGSMEE plate is analysed. Further, the study includes the evaluation of the static behavior of FGSMEE plate for various skew angles. The influence of skew angle on the primary quantities such as displacements, electric potential, and magnetic potential, and secondary quantities such as stresses, electric displacement and magnetic induction is studied in detail. In addition, the effect of power-law gradient, thickness ratio, boundary conditions and aspect ratio on the free vibration and static response characteristics of FGSMEE plate has been investigated.

• Structural Engineering and Mechanics
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• v.70 no.2
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• pp.179-197
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• 2019

In this article, the effect of different geometrical, materials and load parameters on the transient response of axisymmetric viscoelastic functionally graded annular plates with different boundary conditions are studied. The behavior of the plate is assumed the elastic in bulk and viscoelastic in shear with the standard linear solid model. Also, the graded properties vary through the thickness according to a power law function. Three types of mostly applied transient loading, i.e., step, impulse, and harmonic with different load distribution respect to radius coordinate are examined. The motion equations and the corresponding boundary conditions are extracted by applying the first order shear deformation theory which are three coupled partial differential equations with variable coefficients. The resulting motion equations are solved analytically using the perturbation technique and the generalized Fourier series. The sensitivity of the response to the graded indexes, different transverse loads, aspect ratios, boundary conditions and the material properties are investigated too. The results are compared with the finite element analysis.

• Steel and Composite Structures
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• v.13 no.2
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• pp.187-206
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• 2012

In this study, fracture analysis of orthotropic FGM (Functionally Graded Material) plate having center crack is performed, numerically. Material axis arbitrarily oriented and there is an angle ${\theta}^{\circ}$ between material and crack axes. Stress intensity factors at the crack tips for Mode I are calculated using Displacement Correlation Method (DCM). In numerical analysis, effects of material properties and variation of angle ${\theta}^{\circ}$ between material and crack axes on the fracture behavior are investigated for four different boundary conditions. Consequently, it is found that the effect of ${\theta}^{\circ}$ on stress intensity factor depends on variation of material properties.

• Wind and Structures
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• v.22 no.4
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• pp.429-454
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• 2016

In this paper, a shear deformation plate theory based on neutral surface position is developed for free vibration analysis of functionally graded material (FGM) plates. The material properties of the FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents. During manufacture, defects such as porosities can appear. It is therefore necessary to consider the vibration behavior of FG plates having porosities in this investigation. The proposed theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components, in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The neutral surface position for a functionally graded plate which its material properties vary in the thickness direction is determined. The equation of motion for FG rectangular plates is obtained through Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Numerical results are presented and the influences of the volume fraction index and porosity volume fraction on frequencies of FGM plates are clearly discussed.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.707-727
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• 2016

In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.

• Smart Structures and Systems
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• v.22 no.3
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• pp.303-314
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• 2018

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

• Earthquakes and Structures
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• v.10 no.6
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• pp.1429-1449
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• 2016

The effect of porosity on bending and free vibration behavior of simply supported functionally graded plate reposed on the Winkler-Pasternak foundation is investigated analytically in the present paper. The modified rule of mixture covering porosity phases is used to describe and approximate material properties of the FGM plates with porosity phases. The effect due to transverse shear is included by using a new refined shear deformation theory. The number of unknown functions involved in the present theory is only four as against five or more in case of other shear deformation theories. The Poisson ratio is held constant. Based on the sinusoidal shear deformation theory, the position of neutral surface is determined and the equation of motion for FG rectangular plates resting on elastic foundation based on neutral surface is obtained through the minimum total potential energy and Hamilton's principle. The convergence of the method is demonstrated and to validate the results, comparisons are made with the available solutions for both isotropic and functionally graded material (FGM). The effect of porosity volume fraction on Al/Al2O3 and Ti-6Al-4V/Aluminum oxide plates are presented in graphical forms. The roles played by the constituent volume fraction index, the foundation stiffness parameters and the geometry of the plate is also studied.

• Steel and Composite Structures
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• v.49 no.4
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• pp.431-440
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• 2023

The functionally graded (FG) porous plates are usually characterized by the non-symmetric elastic modulus distribution through the thickness so that the plate neutral surface does not coincide with the mid-surface. Nevertheless, the conventional analysis models were mostly based on the plate mid-surface so that the accuracy of resulting numerical results is questionable. In this context, this paper presents the neutral surface-based static and free vibration analysis of FG porous plates and investigates the differences between the mid- and neutral surface-based analysis models. The neutral surface-based numerical method is formulated using the (3,3,2) hierarchical model and approximated by the last introduced natural element method (NEM). The volume fractions of metal and ceramic are expressed by the power-law function and the cosine-type porosity distributions are considered. The proposed numerical method is demonstrated through the benchmark experiment, and the differences between two analysis models are parametrically investigated with respect to the thickness-wise material and porosity distributions. It is found from the numerical results that the difference cannot be negligible when the material and porosity distributions are remarkably biased in the thickness direction.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.431-448
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• 2012

In this paper, the first-order shear deformation theory (FSDT) (Mindlin) for continuum incorporating surface energy is exploited to study the static behavior of ultra-thin functionally graded (FG) plates. The size-dependent mechanical response is very important while the plate thickness reduces to micro/nano scales. Bulk stresses on the surfaces are required to satisfy the surface balance conditions involving surface stresses. Unlike the classical continuum plate models, the bulk transverse normal stress is preserved here. By incorporating the surface energies into the principle of minimum potential energy, a series of continuum governing differential equations which include intrinsic length scales are derived. The modifications over the classical continuum stiffness are also obtained. To illustrate the application of the theory, simply supported micro/nano scaled rectangular films subjected to a transverse mechanical load are investigated. Numerical examples are presented to present the effects of surface energies on the behavior of functionally graded (FG) film, whose effective elastic moduli of its bulk material are represented by the simple power law. The proposed model is then used for a comparison between the continuum analysis of FG ultra-thin plates with and without incorporating surface effects. Also, the transverse shear strain effect is studied by a comparison between the FG plate behavior based on Kirchhoff and Mindlin assumptions. In our analysis the residual surface tension under unstrained conditions and the surface Lame constants are expected to be the same for the upper and lower surfaces of the FG plate. The proposed model is verified by previous work.