• Steel and Composite Structures
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• v.18 no.2
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• pp.425-442
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• 2015

This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures.

• Computers and Concrete
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• v.33 no.1
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• pp.27-39
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• 2024

In this study, the authors investigate the free vibration behavior of three-phases functionally graded sandwich plates using a novel nth-order shear deformation theory. These plates are composed of a homogeneous core and two face-sheet layers made of different functionally graded materials. This is the novel type of the sandwich structures that can be applied in many fields of mechanical engineering and industrial. The proposed theory only requires four unknown displacement functions, and the transverse displacement does not need to be separated into bending and shear parts, simplifying the theory. One noteworthy feature of the proposed theory is its ability to capture the parabolic distribution of transverse shear strains and stresses throughout the plate's thickness while ensuring zero values on the two free surfaces. By eliminating the need for shear correction factors, the theory further enhances computational efficiency. Equations of motion are established using Hamilton's principle and solved via Navier's solution. The accuracy and efficiency of the proposed theory are verified by comparing results with available solutions. The authors then use the proposed theory to investigate the free vibration characteristics of three-phases functionally graded sandwich plates, considering the effects of parameters such as aspect ratio, side-to-thickness ratio, skin-core-skin thicknesses, and power-law indexes. Through careful analysis of the free vibration behavior of three-phases functionally graded sandwich plates, the work highlighted the significant roles played by individual material ingredients in influencing their frequencies.

• Wind and Structures
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• v.26 no.4
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• pp.205-214
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• 2018

In this paper, the thermo-mechanical buckling characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form and the material properties are assumed to be temperature-dependent. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal governing equations are derived based on Timoshenko beam theory through Hamilton's principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared to some cases in the 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 material distribution profile, small scale effects and aspect ratio on the critical buckling temperature of the FG nanobeams in detail. It is explicitly shown that the thermal buckling of a FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

• 한국전산유체공학회:학술대회논문집
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• 2009.11a
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• pp.223-227
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• 2009

In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.

• 한국전산유체공학회:학술대회논문집
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• 1998.11a
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• pp.84-89
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• 1998

This paper describes aerodynamic heating on a hypersonic vehicle. For this purpose, the 2-D, and 3-D equilibrium code are developed. In order to obtain an accurate solution, AUSMPW+ is used for spatial discretization. Curve fitting data in NASA Reference Publication 1181, 1260 are used to calculate equilibrium properties. To observe aerodynamic heating phenomena, Reynolds number parametric study for diamond airfoil is done, 3-D full Navier-Stokes equation is computed and wall temperature distribution data are obtained. Analyzing these results, we conclude that Reynolds number and secondary flow are important factors in aerodynamic heating.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.33 no.3
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• pp.170-177
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• 2009

In the present study, a finite element analysis of conjugate heat transfer problem inside a cavity with a heat-generating conducting body, where constant heat flux is generated, is conducted. A conduction heat transfer problem inside the solid body is automatically coupled with natural convection inside the cavity by using a finite element formulation. A finite element formulation based on SIMPLE type algorithm is adopted for the solution of the incompressible Navier-Stokes equations coupled with energy equation. The proposed algorithm is verified by solving the benchmark problem of conjugate heat transfer inside a cavity having a centered body. Then a conjugate natural heat transfer problem inside a cavity having a heat-generating conducting body with constant heat flux is solved and the effect of the Rayleigh number on the heat transfer characteristics inside a cavity is investigated.

• Steel and Composite Structures
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• v.16 no.5
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• pp.507-519
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• 2014

In this paper, a higher order shear deformation beam theory is developed for static and free vibration analysis of functionally graded beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded beam are assumed to vary according to power law distribution of the volume fraction of the constituents. Based on the present higher-order shear deformation beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Different higher order shear deformation theories and classical beam theories were used in the analysis. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Wind and Structures
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• v.23 no.1
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• pp.59-73
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• 2016

In this paper, a hyperbolic shear deformation beam theory is developed for free vibration analysis of functionally graded (FG) sandwich beams. The theory account for higher-order variation of transverse shear strain through the depth of the beam and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. The material properties of the functionally graded sandwich beam are assumed to vary according to power law distribution of the volume fraction of the constituents. The core layer is still homogeneous and made of an isotropic material. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain frequencies. Illustrative examples are given to show the effects of varying gradients and thickness to length ratios on free vibration of functionally graded sandwich beams.

• Structural Engineering and Mechanics
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• v.69 no.6
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• pp.637-649
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• 2019

In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton's principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.

• Structural Engineering and Mechanics
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• v.77 no.2
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• pp.217-229
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• 2021

The effect of distribution shape of porosity using a quasi-3D theory for free vibration analysis of FG microbeams is studied analytically in the present paper. The microbeams are simply-supported and nonhomogeneous, with power function variation of Young's modulus along their thickness. The modified coupled stress theory is utilized to consolidate size dependency of microbeam. Both even and uneven distribution shape of porosity are considered and the effective properties of porous FG microbeams are defined by theoretical formula with an additional term of porosity. The equation of motion is obtained through Hamilton's principle, however, Navier type solution method is used to obtain frequencies. The influences played by many parameters are also investigated.