• Advances in nano research
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• 제14권5호
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• pp.421-433
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• 2023

In the present paper, the influences of the variation of exponent of volume fraction of carbon nanotubes (CNTs) on the natural frequencies (NFs) of the carbon nanotube-reinforced composite (CNTRC) beams under four different boundary conditions (BCs) are investigated. The single-walled carbon nanotubes (SWCNTs) are assumed to be aligned and dispersed in a polymeric matrix with various reinforcing patterns, according to the variation of exponent of volume fraction of CNTs for functionally graded (FG) reinforcements. Besides, uniform distribution (UD) of reinforcement is also considered to analyze the influence of the non-linear (NL) variation of the reinforcement of CNTs. Using Hamilton's principle and third-order shear deformation theory (TSDT), the equations of motion of the CNTRC beam are derived. Under four different BCs, the resulting equations are solved analytically. To verify the present formulation, comparison investigations are conducted. To examine the impacts of several factors on the NFs of the CNTRC beams, numerical examples and some benchmark results are presented.

• Journal of Advanced Marine Engineering and Technology
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• 제29권7호
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• pp.779-784
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• 2005

This paper presents the theory of similarity transformations applied to the momentum and energy equations for laminar, forced, external boundary layer flow over a horizontal flat plate which leads to a set of non-linear, ordinary differential equations of phase change material slurry(PCM Slurry). The momentum and energy equation set numerically to obtain the non-dimensional velocity and temperature profiles in a laminar boundary layer are solved. The heat transfer characteristics of PCM slurry was numerically investigated with similar method. It is clarified that the similar solution method of Newtonian fluid can be used reasonably this type of PCM slurry which has low concentration. The data of local wall heat flux and convective heat transfer coefficient of PCM slurry are higher than those of water more than 150$\~$200$\%$, approximately.

• 한국해양공학회:학술대회논문집
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• 한국해양공학회 2000년도 춘계학술대회 논문집
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• pp.75-80
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• 2000

We revisit the arrested Ekman boundary layer problem, using a fully non-linear numerical model with the subgrid dissipation modeled by the large eddy simulation method (LES). The main objective of this study is to find out whether the dynamic balance of the arrested Ekman boundary layer explained by MacCready and Rhines (1991) is valid for high Reynolds number. The model solution indicates that for high Reynolds number and low Richardson number flows, the density anomaly diffusion by near-wall turbulent action may become intense enough to homogenize completely the density structure within the boundary layer, in the direction perpendicular to the sloping wall. Then the buoyancy effect becomes negligible allowing a near-equilibrium Ekman boundary layer flow to persist for a long period.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.369-376
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• 2000

For the general loading condition and boundary condition, it is very difficult to obtain closed-form solutions for buckling loads and natural frequencies of thin-walled structures because its behaviour is very complex due to the coupling effect of bending and torsional behaviour. Consequently most of previous finite element formulations introduced approximate displacement fields using shape functions as Hermitian polynomials, isoparametric interpoation function, and so on. The purpose of this study is to calculate the exact displacement field of a thin-walled straight beam element with the non-symmetric cross section and present a consistent derivation of the exact dynamic stiffness matrix. An exact dynamic element stiffness matrix is established from Vlasov's coupled differential equations for a uniform beam element of non-symmetric thin-walled cross section. This numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. The natural frequencies are evaluated for the non-symmetric thin-walled straight beam structure, and the results are compared with available solutions in order to verify validity and accuracy of the proposed procedures.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.165-181
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• 2004

Based on Landau-type transformation, a Stefan problem with non-linear free boundary condition is transformed into a system consisting of parabolic equation and the ordinary differential equations. Semidiscrete approximations are constructed. Optimal orders of convergence of semidiscrete approximation in $L_2$, $H^1$ and $H^2$ normed spaces are derived.

• 대한수학회보
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• 제49권4호
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• pp.737-748
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• 2012

The goal of this paper is to study the existence of non-trivial non-negative weak solution for the nonlinear elliptic equation: $$-div(h(x){\nabla}u)=f(x,u)\;in\;{\Omega}$$ with Dirichlet boundary condition in a bounded domain ${\Omega}{\subset}\mathbb{R}^N$, $N{\geq}3$, where $h(x){\in}L^1_{loc}({\Omega})$, $f(x,s)$ has asymptotically linear behavior. The solutions will be obtained in a subspace of the space $H^1_0({\Omega})$ and the proofs rely essentially on a variation of the mountain pass theorem in [12].

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• 대한전기학회논문지:전기기기및에너지변환시스템부문B
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• 제49권7호
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• pp.457-461
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• 2000

The finite element method (FEM) is suitable for the analysis of a complicated region that includes nonlinear materials, whereas the boundary element method (BEM) is naturally effective for analyzing a very large region with linear characteristics. Therefore, considering the advantages in both methods, a novel algorithm for the alternate application of the FEM and BEM to magnetic field problems with the open boundary is presented. This approach avoids the disadvantages of the typical numerical methods with the open boundary problem such as a great number of unknown values for the FEM and non-symmetric matrix for the Hybrid FE-BE method. The solution of the overall problems is obtained by iterative calculations accompanied with the new acceleration method.

• Computers and Concrete
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• 제14권1호
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• pp.41-57
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• 2014

Modern trend in structural design is to use smaller elements in order to ensure several purposes such as economy, functionality and aesthetic in appearance. However, because of decreasing rigidity of the structural elements, the system displacements increases and displacements become an important subject in this kind of structures takes into account both geometrical changes and the carrying capacity of the material after linear-elastic boundary. In this study, a method is proposed to calculate the failure loads and to analyse the reinforced concrete space frame systems. The numerical examples gathered from the literature survey are solved with this method utilising the prepared computer program and the comparable results are presented. The results show that the method is sufficiently accurate.

• Advances in materials Research
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• 제4권1호
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• pp.31-44
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• 2015

This paper presents a simple n-order four variable refined theory for buckling analysis of functionally graded plates. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The present theory is variationally consistent, uses the n-order polynomial term to represent the displacement field, does not require shear correction factor, and eliminates the shear stresses at the top and bottom surfaces. A power law distribution is used to describe the variation of volume fraction of material compositions. Equilibrium and stability equations are derived based on the present n-order refined theory. The non-linear governing equations are solved for plates subjected to simply supported boundary conditions. The thermal loads are assumed to be uniform, linear and non-linear distribution through-the-thickness. The effects of aspect and thickness ratios, gradient index, on the critical buckling are all discussed.