• Earthquakes and Structures
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• v.17 no.1
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• pp.31-37
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• 2019

This work presents a free vibration analysis of functionally graded beams by employing an original high order shear deformation theory (HSDBT). This theory use only three unknowns, but it satisfies the stress free boundary conditions on the top and bottom surfaces of the beam without requiring any shear correction factors. The mechanical properties of the beam are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. In order to investigate the free vibration response, the equations of motion for the dynamic analysis are determined via the Hamilton's principle. The Navier solution technique is adopted to derive analytical solutions for simply supported beams. The accuracy and effectiveness of proposed model are verified by comparison with previous research.

• Earthquakes and Structures
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• v.17 no.3
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• pp.329-336
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• 2019

An efficient shear deformation beam theory is developed for thermo-elastic vibration of FGM beams. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the on the surfaces of the beam without using shear correction factors. The material properties of the FGM beam are assumed to be temperature dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity are considered through the beam thickness. Based on the present refined beam theory, the equations of motion are derived from Hamilton's principle. The closed-form solutions of functionally graded beams are obtained using Navier solution. Numerical results are presented to investigate the effects of temperature distributions, material parameters, thermal moments and slenderness ratios on the natural frequencies. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.217-231
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• 2023

The bending analysis of sandwich functionally graded (FG) beams under temperature circumstances is performed in this article utilizing Navier's solution-based parabolic shear deformation theory. For the first time, a comparative study has been carried out between the exponential and sigmoidal sandwich FGM beams under thermal conditions. During this investigation, temperature-dependent material characteristics are postulated. Both symmetric and unsymmetric sandwich examples have been studied. The effect of gradation law, gradation coefficient, and thickness scheme on beam behavior has been thoroughly investigated. Three possible temperature combinations at the top and bottom surfaces of the beam are also investigated. Beams with a higher proportion of ceramic to metal are shown to be more resistant to thermal stresses than beams with a higher proportion of metal.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.383-405
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• 2004

We study the incomprssible Navier Stokes equations for the flow inside contraction geometry. The governing equations are expressed in the vorticity-stream function formulations. A rectangular computational domain is arised by elliptic grid generation technique. The numerical solution is based on a technique of automatic numerical generation of acurvilinear coordinate system by transforming the governing equation into computational plane. The transformed equations are approximated using central differences and solved simultaneously by successive over relaxation iteration. The time dependent of the vorticity equation solved by using explicit marching procedure. We will apply the technique on several irregular-shapes.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1483-1504
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• 2017

We consider weak solutions of the instationary Navier-Stokes system in a smooth bounded domain ${\Omega}{\subset}{\mathbb{R}}^3$ with initial value $u_0{\in}L^2_{\sigma}({\Omega})$. It is known that a weak solution is a local strong solution in the sense of Serrin if $u_0$ satisfies the optimal initial value condition $u_0{\in}B^{-1+3/q}_{q,s_q}$ with Serrin exponents $s_q$ > 2, q > 3 such that ${\frac{2}{s_q}}+{\frac{3}{q}}=1$. This result has recently been generalized by the authors to weighted Serrin conditions such that u is contained in the weighted Serrin class ${{\int}_0^T}({\tau}^{\alpha}{\parallel}u({\tau}){\parallel}_q)^s$ $d{\tau}$ < ${\infty}$ with ${\frac{2}{s}}+{\frac{3}{q}}=1-2{\alpha}$, 0 < ${\alpha}$ < ${\frac{1}{2}}$. This regularity is guaranteed if and only if $u_0$ is contained in the Besov space $B^{-1+3/q}_{q,s}$. In this article we consider the limit case of initial values in the Besov space $B^{-1+3/q}_{q,{\infty}}$ and in its subspace ${{\circ}\atop{B}}^{-1+3/q}_{q,{\infty}}$ based on the continuous interpolation functor. Special emphasis is put on questions of uniqueness within the class of weak solutions.

• Journal of the Korean Society of Industry Convergence
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• v.5 no.1
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• pp.45-52
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• 2002

In this study, an exact solution of governing differential equation for the bending problem of partially loaded orthotropic rectangular plates is presented and also its computer program is developed. The method requires that two opposite edges be clamped or simply supported, or one edge clamped and the other simply supported. Any combination of boundary conditions could exist along the other edges. The plate could he subjected to uniform, partially uniform, and line loads. The solution for the deflection of rectangular plate is expressed as a Levy type single Fourier series and the loads arc expressed as a corresponding series. The advantage of the solution is that it overcomes the limitations of the previous Navier's and Levy's methods (limitation of boundary condition and loading conditions of plate), it is easy to program on a computer and it becomes fast to solve the bending problem with computer program. Calculations are presented for isotropic and orthotropic plates with different loading and boundary conditions. Comparisons are made for the isotropic plate with various boundary conditions between the result of this paper and the result of Navier, Levy and Szilard. The deflections were in excellent agreement.

• Advances in materials Research
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• v.7 no.2
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• pp.119-136
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• 2018

In this paper, static and vibration analysis for anti-symmetric cross-ply and angle- ply carbon/glass hybrid laminates rectangular composite plate are presented. In this analysis, the equations of motion for simply supported thick laminated hybrid rectangular plates are derived and obtained through the use of Hamilton's principle. The closed-form solutions of anti-symmetric cross-ply and angle- ply laminates are obtained using Navier solution. The effects of side-to-thickness ratio, aspect ratio, and lamination schemes on the fundamental frequencies loads are investigated. The study concludes that shear deformation laminate theories accurately predict the behavior of composite laminates, whereas the classical laminate theory over predicts natural frequencies. The excellent accuracy of the present analytical solution is confirmed by making some comparisons of the present results with those available in the literature. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behaviors of anti-symmetric cross-ply and angle- ply hybrid laminated composite plates.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.15 no.4
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• pp.661-674
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• 2002

The objective of this study is to develop efficient numerical method to enable solution of optimal control problems of Navier-Stokes flows and to apply these technique to the problem of viscous drag minimization on a bluff body by controlling boundary velocities on the surface of the body. In addition to the industrial importance of the drag reduction problem, it serves as a model for other more complex flow optimization settings, and allows us to study, modify, and improve the behavior of the optimal control methods proposed here. The control is affected by the suction or injection of fluid on portions of the boundary, and the objective function represents the rate at which energy is dissipated in the fluid. This study shows how reduced Hessian successive quadratic programming method, which avoid converging the flow equations at each iteration, can be tailored to these problems.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.112-122
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• 1996

A finite element scheme using the concept of PISO method has been developed to solve the Navier-Stokes viscous flows in all speed range. This scheme includes development of new pressure equation that retains both the hyperbolic term related with the density variation and the elliptic term reflecting the incompressibility constraint. The present method is applied to the incompressible two-dimensional driven cavity flow problems(Re=100, 400 and 1,000). For compressible flows, the Carter plate problem(M=3 and Re=1,000) is computed. Finally, we have simulated the shock-boundary layer interaction(M=2 and Re=2.96×10/sup 5/), a more difficult problem, and compared its results with the experiment to demonstrate the shock capturing capability of the present solution algorithm.

• Journal of computational fluids engineering
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• v.1 no.1
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• pp.123-141
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• 1996

In this paper the upwind flux difference splitting Navier-Stokes method has been applied to study the perfect gas and the equilibrium chemically reacting hypersonic flow over an axisymmetric sphere-cone(5°) geometry. The effective gamma(γ), enthalpy to internal energy ratio was used to couple chemistry with the fluid mechanics for equilibrium chemically reacting air. The test case condition was at altitude(30km) and Mach number(15). The equilibrium shock thickness over the blunt body region was much thinner than that of perfect gas shock. The pressure difference between perfect gas and equilibrium gas was about 3 ∼ 5 percent. The heat transfer coefficient were also calculated. The results were compared with VSL results in order to validate the current numerical analysis. The results from current method were compared well VSL results ; however, not well at near nose. The proper boundary condition and grid system will be studied to improve the solution quality.