• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2011.04a
• /
• pp.635-638
• /
• 2011

유한요소법은 편미분방정식(Partial Differential Equation)의 수치적 근사 해를 구하기 위한 가장 일반적이고 효율적인 방법으로 다양한 공학 분야에서 널리 사용되어지고 있다. 유한요소법의 해석은 연속적인 범위를 가지는 문제를 여러 개의 요소로 나누어 다항식의 형상함수를 만들게 되며 결과적으로 근사 해를 구하게 된다. 이때 해석의 정확성을 높이기 위하여 형상함수의 차수를 높이고 요소의 개수를 늘리게 되면, 이에 따른 수치 계산량의 급격한 증가로 인해 수치해석의 효율성은 떨어지게 된다. 이를 보완하기 위해 유한요소법에 영역분할기법을 적용하여 병렬해석을 수행하면 해의 정확성과 효율성을 동시에 높인다. 병렬해석을 수행하는데 있어서 클러스터의 구조적 특성은 해석의 효율성에 영향을 미치게 된다. 따라서 본 논문에서는 일반적인 모델에 대하여 병렬해석의 수행을 통하여 클러스터의 구조적 특성이 병렬해석의 효율성에 미치는 영향에 대해 확인한다.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.14 no.6
• /
• pp.1408-1416
• /
• 1990

A powerful and efficient method for finding approximate solutions to initial-boundary-value problems in the transient coupled thermoelasticity is formulated in time domain using the finite element technique with time-marching strategy. The final system equations can be derived by the Guritin's variational principle using the definition of convolution integral. But, the finite element formulation for the equations of motion is modified by differentiating in time. Numerical results to some test problems are compared with analytical and other sophisticated approximate solutions. Stable responces are observed in all the given examples irrespective of incremental time steps and mesh shapes. In addition, it is shown that good numerical results are obtained even in coarser mesh or larger time step comparing to other numerical methods.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.22 no.1
• /
• pp.9-17
• /
• 2021

Curved beams are increasingly used in buildings, vehicles, ships, and aircraft, which has resulted in considerable effort being directed toward developing an accurate method for analyzing the dynamic behavior of such structures. The stability behavior of elastic circular arches has been the subject of a large number of investigations. One of the efficient procedures for the solution of ordinary differential equations or partial differential equations is the differential quadrature method DQM. This method has been applied to a large number of cases to overcome the difficulties of the complex computer algorithms, as well as excessive use of storage due to conditions of non-linear geometries, loadings, or material properties. This study uses DQM to analyze the in-plane vibration of the circular arches considering the effects of midsurface extension and rotatory inertia. Fundamental frequency parameters are calculated for the member with various parameter ratios, boundary conditions, and opening angles. The solutions from DQM are compared with exact solutions or other numerical solutions for cases in which they are available and given to analyze the effects of midsurface extension and rotatory inertia on the frequency parameters of the circular arches.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.2
• /
• pp.87-95
• /
• 2018

This paper introduces a new explicit spectral element method for the simulation of SH-waves in semi-infinite domains. To simulate the wave motion in unbounded domains, it is necessary to reduce the infinite extent to a finite computational domain of interest. To prevent the wave reflection from the trunctated boundaries, perfectly matched layer(PML) wave-absorbing boundary is introduced. The forward problem for simulating SH-waves in PML-truncated domains can be formulated as second-order PDEs. The second-order semi-discrete form of the governing PDEs is constructed by using a mixed spectral elements with Legendre-gauss-Lobatto quadrature method, which results in a diagonalized mass matrix. Then the second-order semi-discrete form is transformed to a first-order, whose solutions are calculated by the fourth-order Runge-Kutta method. Numerical examples showed that solutions of SH-wave in the two-dimensional analysis domain resulted in stable and accurate, and reflections from truncated boundaries could be reduced by using PML boundaries. Elastic wave propagation analysis using explicit time integration method may be apt for solving larger domain problems such as three-dimensional elastic wave problem more efficiently.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
• /
• 1995.11a
• /
• pp.50-55
• /
• 1995

향상되어진 93-PCGC-2는 기존의 PCGC-2와 같이 미분탄 연소를 포함하는 다양한 반응성흐름과 비반응성 흐름을 설명하기 위해 2차원 정상상태 모델로 제시되어 졌다. 93-PCGC-2는 실린더형의 축 대칭계에 응용되어질 수 있고, 난류(Turbulence)는 유체역학식과 연소기구 양쪽을 위해 고려되어졌으며, 불연속 세로좌표 방법(Discrete Ordinates Method)을 이용하여 기체, 벽 및 입자들로부터의 복사열(Radiation)을 모사하였다. 입자상은 입자 무리들의 평균 경로들을 따라 해석하는 Lagrangian계의 해석법으로 모델화되어졌다. 석탄의 팽윤(Swelling)과 촤의 반응성에 관한 부모델과 더불어 새롭게 일반화된 석탄 탈휘발화 부모델 (FG-DVC)도 첨가되어졌다. 비균일 반응기구는 확산과 화학반응 둘 모두를 고려하였다. 주요 기상반응은 국부 순간 평형을 가정하여 모델화하였다. 그래서 반응속도는 혼합의 난류속도에 의해 제한되어진다. Thermal NOx과 Fuel NOx의 유한속도 화학론(Finite Rate Chemstry)에 대한 부모델은 화학반응속도론와 난류성의 통계치를 통합하여 만들어져 있다. 기상은 반복적인 line-by-line기교에 의해 풀려지는 elliptic partial differential equation으로 묘사되어진다. 수치적인 안정을 고려하기 위해 under-relaxation이 이용되어졌다. 이렇게 코드화된 93-PCGC-2는 연소를 위해 모사되어졌다. 또한 더 나아가 이 수치모델의 활용범위는 미분탄의 가스화에도 활용되어질 것으로 기대되어진다.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.33 no.1
• /
• pp.13-22
• /
• 2013

This paper deals with a novel method for numerical analyses of the tapered geometrical non-linear beam with three unknown parameters, subjected a floating point load. The beams with hinged-movable end constraint are chosen as the objective beam. Cross sections of the beam whose flexural rigidities are functionally varied with the axial coordinate. The first order simultaneous differential equations governing the elastica of such beam are derived on the basis of the Bernoulli-Euler beam theory. A novel numerical method for solving these equations is developed by using the iteration technique. The processes of the solution method are extensively discussed through a typical numerical example. For validating theories developed herein, laboratory scaled experiments are conducted.

• Journal of the Korean Geosynthetics Society
• /
• v.18 no.3
• /
• pp.69-77
• /
• 2019

This paper presents a new analytical model for estimating the free vibration of tapered friction piles. The governing differential equation for the free vibration of statically axially-loaded piles embedded in non-homogeneous soil is derived. The equation is numerically integrated by the Runge-Kutta method, and then the eigenvalue of natural frequency is determined by the Regula-Falsi scheme. For a cylindrical non-tapered pile, the computed natural frequencies compare well with the available data from literature. Numerical examples are presented to investigate the effects of the tapering, the skin friction resistance, the end condition of the pile, the vertical compressive loading, and the soil non-homogeneity on the natural frequency and mode shape of tapered friction piles.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1998.10a
• /
• pp.97-100
• /
• 1998

옵션의 가격을 계산하기 위한 수치해법은 크게 격자모형, 유한차분법, 그리고 몬테카를로 시뮬레이션의 세 가지로 분류된다. 유한차분법은 옵션가격함수가 만족하는 편미분 방정식의 모든 편도함수를 유한 차분식으로 근사하여 옵션을 평가하는 방법이다. 본 연구에서는 유한차분법을 이용하여 옵션을 평가 할 때 발생하는 가격계산 오차의 가장 큰 원인이 옵션 만기 손익구조(payoff)의 비선형성에 있음을 보인다. 특히, 옵션 시장에서 가장 거래가 많이 이루어지는 손익분기옵션(at the money option) 그리고 손익분기점에 가까운 옵션(around the money option)에서 가장 큰 오차가 발생함을 보인다. 또한 본 연구에서는 이러한 오차를 효율적으로 줄이기 위하여 행사가격 근처의 일부 구간에서만 구간점 사이의 간격을 변화시키는 수정된 유한차분법을 제시하고 오차의 크기와 계산의 효율성 측면에서 기존의 유한차분법과 비교·분석한다.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.617-621
• /
• 2001

This paper presents the application of the technique of differential transformation to find the vibration frequencies for inhomogeneous beams with one sliding support, the other clamped and the other pinned boundary conditions. Numerical calculations are carried out. The frequencies obtained from the differential-transformation solutions are compared to published results to demonstrate the accuracy and flexibility of the method.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.13 no.4
• /
• pp.251-258
• /
• 1993

The main purpose of this paper is to present both the natural frequencies and the buckling loads of beam-columns on Winkler-type foundations. The ordinary differential equations governing the free vibrations and the buckling loads of beam-columns on Winkler-type foundation are derived as nondimensional forms. The Runge-Kutta method and Determinant Search method are used to perform the integration of the differential equations and to determine the eigenvalues(natural frequencies and buckling loads), respectively. Hinged-hinged and damped-clamped end constraints are applied in numerical examples. The relation between frequency parameter and elastic foundation parameter is presented in figure. The effects of axial loads on the natural frequencies of beam-columns on elastic foundations are investigated and the relation between buckling load parameter and elastic foundation parameter is also analyzed. The relation between foundation rested ratio and frequency parameter, buckling load parameter are investigated. The beam-columns on non-homogeneous elastic foundation are analyzed and typical mode shapes are also presented.