• Structural Engineering and Mechanics
• /
• v.70 no.1
• /
• pp.55-66
• /
• 2019

This work deals with the size-dependent wave propagation analysis of functionally graded (FG) anisotropic nanoplates based on a nonlocal strain gradient refined plate model. The present model incorporates two scale coefficients to examine wave dispersion relations more accurately. Material properties of FG anisotropic nanoplates are exponentially varying in the z-direction. In order to solve the governing equations for bulk waves, an analytical method is performed and wave frequencies and phase velocities are obtained as a function of wave number. The influences of several important parameters such as material graduation exponent, geometry, Winkler-Pasternak foundation parameters and wave number on the wave propagation of FG anisotropic nanoplates resting on the elastic foundation are investigated and discussed in detail. It is concluded that these parameters play significant roles on the wave propagation behavior of the nanoplates. From the best knowledge of authors, it is the first time that FG nanoplate made of anisotropic materials is investigated, so, presented numerical results can serve as benchmarks for future analysis of such structures.

• Advances in aircraft and spacecraft science
• /
• v.9 no.1
• /
• pp.69-93
• /
• 2022

Reduced graphene oxide (rGO) is one of the derivatives of graphene, which has drawn some experimental research interests in recent years however, numerical research studying the mechanical behaviors of composites made of rGO has not been taken into consideration yet. The objective of this research is to investigate the buckling, and free vibration of functionally graded reduced graphene oxide reinforced nanocomposite (FG rGORC) plates employing isogeometric analysis (IGA). The effective Young's modulus of rGORC is determined based onthe Halpin-Tsai model. Four different FG distribution types of rGO are considered varying across plate thickness. Besides, the refined plate theory is used based on Reddy's third-order function. To capture the size effect, modified couple stress theory (MCST) is employed. A comprehensive study is provided examining the effect of various parameters including rGO weight fraction, FG distribution types, boundary conditions, material length scale parameter, etc. Our obtained results show that the addition of only 1% of uniformly distributed rGO into epoxy plates leads to the fundamental frequency and critical buckling load 18% and 39% higher than those of pure epoxy plates, respectively.

• Structural Engineering and Mechanics
• /
• v.60 no.3
• /
• pp.489-505
• /
• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Steel and Composite Structures
• /
• v.37 no.2
• /
• pp.253-258
• /
• 2020

Vibration response in a sandwich plate with a nanocompiste core covered by magnetic layer is presented. The core is armed by functionalyy graded-carbon nanotubes (FG-CNTs) where the Mori-Tanaka law is utilized assuming agglomeration effects. The structure plate is located on elastic medium simulated by Pasternak model. The governing equations are derived based on Mindlin theory and Hamilton's principle. Utilizing diffrential quadrature method (DQM), the frequency of the structure is calculated and the effects of magnetic layer, volume percent and agglomeration of CNTs, elastic medium and geometrical parameters of structure are shown on the frequency of system. Results indicate that with considering magnetic layer, the frequency of structure is increased.

• Advances in nano research
• /
• v.5 no.2
• /
• pp.69-97
• /
• 2017

In this study, nonlinear response of laminated functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate under low-velocity impact based on the Eshelby-Mori-Tanaka approach in thermal conditions is studied. The governing equations are derived based on higher-order shear deformation plate theory (HSDT) under von $K\acute{a}rm\acute{a}n$ geometrical nonlinearity assumptions. The finite element method with 15 DOF at each node and Newmark's numerical integration method is applied to solve the governing equations. Four types of distributions of the uniaxially aligned reinforcement material through the thickness of the plates are considered. Material properties of the CNT and matrix are assumed to be temperature dependent. Contact force between the impactor and the laminated plate is obtained with the aid of the modified nonlinear Hertzian contact law models. In the numerical example, the effect of layup (stacking sequence) and lamination angle as well as the effect of temperature variations, distribution of CNTs, volume fraction of the CNTs, the mass and the velocity of the impactor in a constant energy level and boundary conditions on the impact response of the CNTRC laminated plates are investigated in details.

• Structural Engineering and Mechanics
• /
• v.78 no.4
• /
• pp.439-453
• /
• 2021

In this work, quasi three-dimensional (quasi-3D) shear deformation theory is presented for bending and dynamic analysis of functionally graded (FG) plates. The effect of varying material properties and volume fraction of the constituent on dynamic and bending behavior of the FG plate is discussed. The benefit of this model over other contributions is that a number of variables is diminished. The developed model considers nonlinear displacements through the thickness and ensures the free boundary conditions at top and bottom faces of the plate without using any shear correction factors. The basic equations that account for the effects of transverse and normal shear stresses are derived from Hamilton's principle. The analytical solutions are determined via the Navier procedure. The accuracy of the proposed formulation is proved by comparisons with the different 2D, 3D and quasi-3D solutions found in the literature.

• Structural Engineering and Mechanics
• /
• v.85 no.2
• /
• pp.147-161
• /
• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• Computers and Concrete
• /
• v.25 no.1
• /
• pp.37-57
• /
• 2020

This work investigates a new type of quasi-3D hyperbolic shear deformation theory is proposed in this study to discuss the statics and free vibration of functionally graded porous plates resting on elastic foundations. Material properties of porous FG plate are defined by rule of the mixture with an additional term of porosity in the through-thickness direction. By including indeterminate integral variables, the number of unknowns and governing equations of the present theory is reduced, and therefore, it is easy to use. The present approach to plate theory takes into account both transverse shear and normal deformations and satisfies the boundary conditions of zero tensile stress on the plate surfaces. The equations of motion are derived from the Hamilton principle. Analytical solutions are obtained for a simply supported plate. Contrary to any other theory, the number of unknown functions involved in the displacement field is only five, as compared to six or more in the case of other shear and normal deformation theories. A comparison with the corresponding results is made to verify the accuracy and efficiency of the present theory. The influences of the porosity parameter, power-law index, aspect ratio, thickness ratio and the foundation parameters on bending and vibration of porous FG plate.

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

• Advances in materials Research
• /
• v.8 no.3
• /
• pp.155-177
• /
• 2019

In this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded sandwich plate with new definition of porosity distribution taking into account composition and the scheme of the sandwich plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Material properties of FGM layers are assumed to vary continuously across the plate thickness according to either power-law or sigmoid function in terms of the volume fractions of the constituents. The face layers are considered to be FG across each face thickness while the core is made of a ceramic homogeneous layer. Governing equations are derived from the principle of virtual displacements. The closed-form solution of a simply supported rectangular plate subjected to sinusoidal loading has been obtained by using the Navier method. Numerical results are presented to show the effect of the material distribution, the sandwich plate geometry and the porosity on the deflections and stresses of FG sandwich plates. The validity of the present theory is investigated by comparing some of the present results with other published results.