• Advances in Computational Design
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• 제5권4호
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• pp.397-416
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• 2020

Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned - clamped (P-C), axial hinge - pinned (AH-P), axial hinge - clamped (AH-C), pinned - shear hinge (P-SHH), pinned - shear force released (P-SHR), axial hinge - shear force released (AH-SHR) and axial hinge - shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.

• 한국안전학회지
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• 제12권4호
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• pp.220-229
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• 1997

곡선보(curved beam)의 등분포 하중하에서 평면내(in-plane)와 평면의(out-of-plane)의 좌굴(buckling)을 해석하는데 differential quadrature method (DQM)을 이용하여 다양한 경계조건(boundary conditions)과 굽힘각(opening angles)에 따른 입계하중(critical loads)을 계산하였다. DQM의 해석결과는 해석적 해답(exact solution) 또는 다른 수지해석 결과와 비교하였으며, DQM은 적은 요소(grid points)를 사용하여 정확한 해석결과를 보여주었다. 두 경계조건(고정-고정, 고정-단순지지)하에서 새로운 결과를 또한 제시하였다.

• 한국산업융합학회 논문집
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• 제5권4호
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• pp.303-307
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• 2002

We consider the problem y"=a(x,y)(y-b), (0$$y(0)=0,\;y^{\prime}(1)=g(y({\xi}),\;y^{\prime}({\xi})),\;{\xi}$$ fixed in (0,1). This is a model of steady-state heat conduction in a rod when the heat flux at the end x=1 is determined by observation of the temperature and heat flux at some interior point ${\xi}$. We establish conditions sufficient for existence, uniqueness, and positivity of solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제14권1호
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• pp.43-56
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• 2010

The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity $u=a+{\nabla}{\phi}$ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and ${\phi}$. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable ${\phi}$. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation.

• 한국군사과학기술학회지
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• 제19권4호
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• pp.424-434
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• 2016

A few blast experiments are conducted to investigate the behavior of one-way reinforced concrete(RC) slabs under blast loading. Reflected blast characteristics as well as displacements and damage patterns of RC slabs are measured. Numerical models are also established in the software ANSYS AUTODYN to reproduce the experiments on RC slabs. The numerical models are distinguished from each other by different boundary conditions at the edges of RC slabs, which are assumed to reproduce displacements and damage patterns resulted from the experiments. The boundary condition of the experimental tests is estimated from the numerical simulation results. From the numerical simulation results, the boundary condition should be improved in order to measure the accurate maximum displacement in the experimental tests.

• Wind and Structures
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• 제5권2_3_4호
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• pp.379-392
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• 2002

Numerical flow computations around an aeroelastic 3D square cylinder immersed in the turbulent boundary layer are shown. Present computational code can be characterized by three numerical aspects which are 1) the method of artificial compressibility is adopted for the incompressible flow computations, 2) the domain decomposition technique is used to get better grid point distributions, and 3) to achieve the conservation law both in time and space when the flow is computed a with moving and transformed grid, the time derivatives of metrics are evaluated using the time-and-space volume. To provide time-dependant inflow boundary conditions satisfying prescribed time-averaged velocity profiles, a convenient way for generating inflow turbulence is proposed. The square cylinder is modeled as a 4-lumped-mass system and it vibrates with two-degree of freedom of heaving motion. Those blocks which surround the cylinder are deformed according to the cylinder's motion. Vigorous oscillations occur as the vortex shedding frequency approaches cylinder's natural frequencies.

• 한국생산제조학회지
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• 제4권4호
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• pp.33-41
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• 1995

This study includes thermal plasticity analyses for a turbine rotor with the simple geometry and the boundary conditions. When centrifugal or thermal stress are applied at the high temperature material of engine blade, stress distributions I material ($\sigma$${\gamma}$${\gamma}$, $\sigma$$\theta$$\theta$, $\tau$${\gamma}$$\theta$, Mises stress) are analyzed by computer simulation(ABQUS) as followings; 1. The maximum stress at the radial direction() is applied at the upper middle part of spline hole. 2. The maximum stress at the tangential direction() is applied at the upper right boundary of spline hole. 3. The maximum shear stress () in () direction is applied at the upper middle part of spline hole. 4. The maximum Mises stress is applied at the upper right boundary of spline hole. This stress is due to the critical stress by which rotor can be fractured according to elapsed time.

• Wind and Structures
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• 제27권4호
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• pp.235-245
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• 2018

In this study the stress analysis of orthotropic thin plate with arbitrary shapes for different boundary conditionsis investigated. Meshfreemethod is applied to static analysis of thin plates with various geometries based on the Kirchhoff classical plate theory. According to the meshfree method the domain of the plates are expressed through a set of nodes without using mesh. In this method, a set of nodes are defined in a standard rectangular domain, then via a third order map, these nodes are transferred to the main domain of the original geometry; therefore the analysis of the plates can be done. Herein, Meshless local Petrov-Galerkin (MLPG) as a meshfree numerical method is utilized. The MLS function in MLPG does not satisfy essential boundary conditions using Delta Kronecker. In the MLPG method, direct interpolation of the boundary conditions can be applied due to constructing node by node of the system equations. The detailed parametric study is conducted, focusing on the arbitrary geometries of the thin plates. Results show that the meshfree method provides better accuracy rather than finite element method. Also, it is found that trend of the figures have good agreement with relevant published papers.

• 터널과지하공간
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• 제15권5호
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• pp.330-337
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• 2005

전단하중을 받는 암반의 전단특성은 절리면의 구조적인 특징뿐만 아니라 암반 주변의 경계조건에 의해서도 영향을 받는다. 암반블록의 경계조건은 절리면이 받고 있는 응력상태를 기준으로 4가지로 구분할 수 있다. 일반적으로 주로 사용되는 CNL 조건의 전단시험에서 얻어지는 전단강도는 다른 경계조건에서 얻어지는 것보다 낮은 전단강도를 나타내며 그 거동도 다른 것으로 나타났다. 본 연구에서는 일정수직하중(CNL) 시험결과를 정규화한 그래픽 방법을 이용하여 일정수직강성(CNS) 조건의 전단거동을 모사할 수 있었다.

• Advances in nano research
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• 제4권2호
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• pp.85-111
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• 2016

In this paper, the classical and non-classical boundary conditions effect on free vibration characteristics of functionally graded (FG) size-dependent nanobeams are investigated by presenting a semi analytical differential transform method (DTM) for the first time. Three kinds of mathematical models, namely; power law (P-FGM), sigmoid (S-FGM) and Mori-Tanaka (MT-FGM) distribution are considered to describe the material properties in the thickness direction. The nonlocal Eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle and they are solved applying semi analytical differential transform method. The good agreement between the results of this article and those available in literature validated the presented approach. 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 small scale effects, spring constant factors, various material compositions and mode number on the normalized natural frequencies of the FG nanobeams in detail. It is explicitly shown that the vibration of FG nanobeams is significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.