• Wind and Structures
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• v.29 no.6
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• pp.457-469
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• 2019

In this paper, a numerical solution is presented for supersonic flutter analysis of cantilever non-symmetric functionally graded (FG) sandwich plates. The plate is considered to be composed of two different functionally graded face sheets and an isotropic homogeneous core made of ceramic. Based on the first order shear deformation theory (FSDT) and linear piston theory, the set of governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and solved numerically using generalized differential quadrature method (GDQM) and critical velocity and flutter frequencies are calculated. For various values of the yaw angle, effect of different parameters like aspect ratio, thickness of the plate, power law indices and thickness of the core on the flutter boundaries are investigated. Numerical examples show that wings and tail fins with larger length and shorter width are more stable in supersonic flights. It is concluded for FG sandwich plates made of Al-Al₂O₃ that increase in volume fraction of ceramic (Al₂O₃) increases aeroelastic stability of the plate. Presented study confirms that improvement of aeroelastic behavior and weight of wings and tail fins of aircrafts are not consistent items. It is shown that value of the critical yaw angle depends on aspect ratio of the plate and other parameters including thickness and variation of properties have no considerable effect on it. Results of this paper can be used in design and analysis of wing and tail fin of supersonic airplanes.

• Steel and Composite Structures
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• v.44 no.1
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• pp.65-79
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• 2022

The main goal of this paper is to study the vibration of damaged core laminated annular plates with FG face sheets based on a three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. In this study the effect of microcracks on the vibrational characteristic of the sandwich plate is considered. In particular, the structures are made by an isotropic core that undergoes a progressive uniform damage, which is modeled as a decay of the mechanical properties expressed in terms of engineering constants. These defects are uniformly distributed and affect the central layer of the plates independently from the direction, this phenomenon is known as "isotropic damage" and it is fully described by a scalar parameter. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular plate is assumed to have any arbitrary boundary conditions at the circular edges including simply supported, clamped and, free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution, and boundary conditions.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.233-246
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• 2023

Bending and buckling analysis of multi-directional porous functionally graded sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. The principle of virtual displacements was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The validation of the present study has been performed with those available in the literature. The composition of metal-ceramic-based FGM changes in longitudinal and transverse directions according to the power law. Different porosity laws, such as uniform distribution, unevenly and logarithmically uneven distributions were used to mimic the imperfections in the functionally graded material that were introduced during the fabrication process. Several sandwich plates schemes were studied based on the plate's symmetry and the thickness of each layer. The effects of grading parameters and porosity laws on the bending and buckling of sandwich plates were examined.

• Structural Engineering and Mechanics
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• v.67 no.3
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• pp.219-232
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• 2018

This paper deals with the static bending of various types of FGM sandwich plates resting on two-parameter elastic foundations in hygrothermal environment. The elastic foundation is modeled as Pasternak's type, which can be either isotropic or orthotropic and as a special case, it converges to Winkler's foundation if the shear layer is neglected. The present FGM sandwich plate is assumed to be made of a fully ceramic core layer sandwiched by metal/ceramic FGM coats. The governing equations are derived from principle of virtual displacements based on a shear and normal deformations plate theory. The present theory takes into account both shear and normal strains effects, thus it predicts results more accurate than the shear deformation plate theories. The results obtained by the shear and normal deformation theory are compared with those available in the literature and also with those obtained by other shear deformation theories. It is concluded that the present results are slightly deviated from other results because the normal deformation effect is taken into account. Numerical results are presented to show the effects of the different parameters, such as side-to-thickness ratio, foundation parameters, aspect ratio, temperature, moisture, power law index and core thickness on the stresses and displacements of the FG sandwich plates.

• Steel and Composite Structures
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• v.49 no.3
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• pp.307-323
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• 2023

In this research, the study of the thermoelastic flexural analysis of silicon carbide/Aluminum graded (FG) sandwich 2D uniform structure (plate) under harmonic sinusoidal temperature load over time is presented. The plate is modeled using a simple two dimensional integral shear deformation plate theory. The current formulation contains an integral terms whose aim is to reduce a number of variables compared to others similar solutions and therefore minimize the computation time. The transverse shear stresses vary according to parabolic distribution and vanish at the free surfaces of the structure without any use of correction factors. The external load is applied on the upper face and varying in the thickness of the plates. The structure is supposed to be composed of "three layers" and resting on nonlinear visco-Pasternak's-foundations. The governing equations of the system are deduced and solved via Hamilton's principle and general solution. The computed results are compared with those existing in the literature to validate the current formulation. The impacts of the parameters (material index, temperature exponent, geometry ratio, time, top/bottom temperature ratio, elastic foundation type, and damping coefficient) on the dynamic flexural response are studied.

• Smart Structures and Systems
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• v.23 no.5
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• pp.429-447
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• 2019

The present study analyzed free vibration of the three-layered micro annular/circular plate which its core and face sheets are made of saturated porous materials and FG-CNTRCs, respectively. The structure is subjected to magneto-electric fields and magneto-electro-mechanical pre loads. Mechanical properties of the porous core and also FG-CNTRC face sheets are varied through the thickness direction. Using dynamic Hamilton's principle, the motion equations based on MCS and FSD theories are derived and solved via GDQ as an efficient numerical method. Effect of different parameters such as pores distributions, porosity coefficient, pores compressibility, CNTs distribution, elastic foundation, multi-physical pre loads, small scale parameter and aspect ratio of the plate are investigated. The findings of this study can be useful for designing smart structures such as sensor and actuator.

• Smart Structures and Systems
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• v.20 no.5
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• pp.583-593
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• 2017

This research deals with the nonlocal temperature-dependent dynamic buckling analysis of embedded sandwich micro plates reinforced by functionally graded carbon nanotubes (FG-CNTs). The material properties of structure are assumed viscoelastic based on Kelvin-Voigt model. The effective material properties of structure are considered based on mixture rule. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying Sinusoidal shear deformation theory (SSDT) in which the size effects are considered using Eringen's nonlocal theory. The differential quadrature (DQ) method in conjunction with the Bolotin's methods is applied for calculating resonance frequency and dynamic instability region (DIR) of structure. The effects of different parameters such as volume percent of CNTs, distribution type of CNTs, temperature, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the CNTs have an important role in dynamic stability of structure and FGX distribution type is the better choice.

• Steel and Composite Structures
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• v.32 no.3
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• pp.389-410
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• 2019

In this article, a simple quasi-3D shear deformation theory is employed for thermo-mechanical bending analysis of functionally graded material (FGM) sandwich plates. The displacement field is defined using only 5 variables as the first order shear deformation theory (FSDT). Unlike the other high order shear deformation theories (HSDTs), the present formulation considers a new kinematic which includes undetermined integral variables. The governing equations are determined based on the principle of virtual work and then they are solved via Navier method. Analytical solutions are proposed to provide the deflections and stresses of simply supported FGM sandwich structures. Comparative examples are presented to demonstrate the accuracy of the present theory. The effects of gradient index, geometrical parameters and thermal load on thermo-mechanical bending response of the FG sandwich plates are examined.

• Advances in nano research
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• v.12 no.6
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• pp.593-603
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• 2022

The critical buckling temperature rise of a newly proposed piezoelectrically active sandwich plate (ASP) has been investigated in this work. This structure includes a porous polymeric layer integrated between two piezoelectric nanocomposite layers. The piezoelectric material is made of a passive polymeric material that is activated by lead-free nanowires (NWs) of zinc oxide (ZnO) embedded inside the matrix. In both nanocomposite layers and porous core, functional graded (FG) patterns have been considered for the distributions of ZnO NWs and voids, respectively. By adopting a higher-order theory of plates, the governing equations of thermal buckling are obtained. This set of equations is then treated using an extended mesh-free solution. The effects of plate dimensions, porosity states, and the nanowire parameters have been investigated on the critical buckling temperature rises of the proposed lightweight ASPs with different boundary conditions. The results disclose that the use of porosities in the core and/or mixing ZnO NWs in the face sheets substantially arise the critical buckling temperatures of the newly proposed active sandwich plates.

• Advances in aircraft and spacecraft science
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• v.10 no.1
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• pp.83-106
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• 2023

In this work, the static behavior of FGM macro and nano-plates under thermomechanical loading. Equilibrium equations are determined by using virtual work principle and local and non-local theory. The novelty of the current model is using a new displacement field with four variables and a warping function considering the effect of shear. Through this analysis, the considered sandwich FGM macro and nanoplates are a homogeneous core and P-FGM faces, homogeneous faces and an E-FGM core and finally P-FGM faces and an E-FGM core. The analytical solution is obtained by using Navier method. The model is verified with previous published works by other models and very close results are obtained within maximum 1% deviation. The numerical results are performed to present the influence of the various parameters such as, geometric ratios, material index as well as the scale parameters are investigated. The present model can be applicable for sandwich FG plates used in nuclear, aero-space, marine, civil and mechanical applications.