• 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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• 제51권2호
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• pp.139-151
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• 2024

In this research, a semi-analytical solution is presented for computing mechanical displacements and thermal stresses in rotating thick cylindrical pressure vessels made of functionally graded material (FGM). The modulus of elasticity, linear thermal expansion coefficient, and density of the cylinder are assumed to change along the axial direction as a power-law function. It is also assumed that Poisson's ratio and thermal conductivity are constant. This cylinder was subjected to non-uniform internal pressure and thermal loading. Thermal loading varies in two directions. The governing equations are derived by the first-order shear deformation theory (FSDT). Using the multilayer method, a functionally graded (FG) cylinder with variable thickness is divided into n homogenous disks, and n sets of differential equations are obtained. Applying the boundary conditions and continuity conditions between the layers, the solution of this set of equations is obtained. To the best of the researchers' knowledge, in the literature, there is no study carried out bi-directional thermoelastic analysis of clamped-clamped rotating FGM thick-walled cylindrical pressure vessels under variable pressure in the longitudinal direction.

• Steel and Composite Structures
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• 제46권2호
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• pp.263-277
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• 2023

Free vibration analysis of multi-directional porous functionally graded (FG) sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. Hamilton's principle 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 results obtained are validated with those available in the literature. The composition of metal-ceramic-based functionally graded material (FGM) changes in longitudinal and transverse directions according to the power law. Imperfections in the functionally graded material introduced during the fabrication process were modeled with different porosity laws such as evenly, unevenly distributed, and logarithmic uneven distributions. The effect of porosity laws and geometry parameters on the natural frequency was investigated. On comparing the natural frequency of two cases for perfect and imperfect sandwich plates a reverse trend in natural frequency result was seen. The finding shows a multidirectional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters and imperfection types have been identified which will guide experimentalists and researchers in selecting fabrication routes for improving the performance of such structures.

• 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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• 제52권5호
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• pp.501-513
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• 2024

Two-directional functionally graded materials (2D-FGMs) show extraordinary physical properties which makes them ideal candidates for designing smart micro-switches. Pull-in instability is one of the most critical challenges in the design of electrostatically-actuated microswitches. The present research aims to bridge the gap in the static pull-in instability analysis of microswitches composed of 2D-FGM. Euler-Bernoulli beam theory with geometrical nonlinearity effect (i.e. von-Karman nonlinearity) in conjunction with the modified couple stress theory (MCST) are employed for mathematical formulation. The micro-switch is subjected to electrostatic actuation with fringing field effect and Casimir force. Hamilton's principle is utilized to derive the governing equations of the system and corresponding boundary conditions. Due to the extreme nonlinear coupling of the governing equations and boundary conditions as well as the existence of terms with variable coefficients, it was difficult to solve the obtained equations analytically. Therefore, differential quadrature method (DQM) is hired to discretize the obtained nonlinear coupled equations and non-classical boundary conditions. The result is a system of nonlinear coupled algebraic equations, which are solved via Newton-Raphson method. A parametric study is then implemented for clamped-clamped and cantilever switches to explore the static pull-in response of the system. The influences of the FG indexes in two directions, length scale parameter, and initial gap are discussed in detail.

• Structural Engineering and Mechanics
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• 제85권2호
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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.

• Steel and Composite Structures
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• 제39권5호
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• pp.565-581
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• 2021

In this paper the buckling analysis of the nanoplate made of arbitrary bi-directional functionally graded (BDFG) materials with small scale effects are investigated. To study the small-scale effects on buckling load, the Eringen's nonlocal theory is applied. Employing the principle of minimum potential energy, the governing equations are obtained. Generalize differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the buckling load of BDFG nanoplates. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. Comparison between the results of GDQ method and other papers for buckling analysis of a simply supported rectangular nano FGM plate reveals the accuracy of GDQ method. At the end some numerical results are presented to study the effects of material length scale parameter, plate thickness, aspect ratio, Poisson's ratio boundary condition and side to thickness ratio on size dependent Frequency.

• Structural Engineering and Mechanics
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• 제82권4호
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• pp.477-490
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• 2022

This article investigates the nonlinear behavior of two-directional functionally graded materials (TDFGM) doubly curved panels with porosities for the first time. An improved and effectual approach is established based on the improved first-order shear deformation shell theory (IFSDST) and von Karman's type nonlinearity. The IFSDST considers the effects of shear deformation without the need for a shear correction factor. The composition of TDFGM constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both thickness and longitudinal directions. A nonlinear finite element method in conjunction with Hamilton's principle is used to obtain the governing equations. Then, the direct iterative method is incorporated to accomplish the numerical results using the frequency-amplitude, nonlinear central deflection relations. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, curvature ratio, thickness ratio, and aspect ratio provides a thorough insight into the linear and nonlinear responses of the porous curved panels. Meanwhile, this study emphasizes the influence of the volume fraction gradation profiles in conjunction with the various material and geometrical parameters on the linear frequency, nonlinear frequency, and deflection of the TDFGM porous shells. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in a specified direction with an appropriate combination of materials. Hence, TDFGM panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

• Advances in nano research
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• 제12권3호
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• pp.281-290
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• 2022

In the current research, the thermal buckling characteristics of the bi-directional functionally graded nano-scale tapered beam on the basis of a couple of nonlocal Eringen and classical beam theories are scrutinized. The nonlocal governing equation and associated nonlocal boundary conditions are constructed using the conservation energy principle, and the resulting equations are solved using the generalized differential quadrature method (GDQM). The mechanical characteristics of the produced material are altered along both the beam length and thickness direction, indicating that it is a two-dimensional functionally graded material (2D-FGM). It is thought that the nanostructures are defective because to the presence of porosity voids. Finally, the obtained results are used to design small-scale sensors and make an excellent panorama of developing the production of nanostructures.

• Computers and Concrete
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• 제30권2호
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• pp.85-97
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• 2022

Using a combination of nonlocal Eringen as well as classical beam theories, this research explores the thermal buckling of a bidirectional functionally graded nanobeam. The formulations of the presented problem are acquired by means on conserved energy as well as nonlocal theory. The results are obtained via generalized differential quadrature method (GDQM). The mechanical properties of the generated material vary in both axial and lateral directions, two-dimensional functionally graded material (2D-FGM). In nanostructures, porosity gaps are seen as a flaw. Finally, the information gained is used to the creation of small-scale sensors, providing an outstanding overview of nanostructure production history.