• Structural Engineering and Mechanics
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• 제73권4호
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• pp.455-462
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• 2020

The hybrid method using the extended finite element method (XFEM) and the forward Euler approach is widely employed to predict the fatigue life of plate structures. Due to the accuracy of the forward Euler approach is determined by a small step size, the performance of fatigue life prediction of the hybrid method is not agreeable. Instead the forward Euler approach, a prediction method using midpoint method and support vector regression (SVR) is presented to evaluate the stress intensity factors (SIFs) and the fatigue life. Firstly, the XFEM is employed to calculate the SIFs with given crack sizes. Then use the history of SIFs as a function of either number of fatigue life cycles or crack sizes within the current cycle to build a prediction model. Finally, according to the prediction model predict the SIFs at different crack sizes or different cycles. Three numerical cases composed by a homogeneous plate with edge crack, a composite plate with edge crack and center crack are introduced to verify the performance of the proposed method. The results show that the proposed method enables large step sizes without sacrificing accuracy. The method is expected to predict the fatigue life of complex structures.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.603-618
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• 2022

In this paper, a numerical solution of the generalized diffusion equation with a delay has been obtained by a numerical technique based on the Galerkin finite element method by applying the cubic B-spline basis functions. The time discretization process is carried out using the forward Euler method. The numerical scheme is required to preserve the delay-independent asymptotic stability with an additional restriction on time and spatial step sizes. Both the theoretical and computational rates of convergence of the numerical method have been examined and found to be in agreement. As it can be observed from the numerical results given in tables and graphs, the proposed method approximates the exact solution very well. The accuracy of the numerical scheme is confirmed by computing L₂ and L_∞ error norms.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1179-1189
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• 2016

We provide a combination of the forward Euler method and the trapezoidal quadrature rule leads to a two-step conservative numerical method which possesses TV-stable property together with consistency.

• Structural Engineering and Mechanics
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• 제30권3호
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• pp.369-382
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• 2008

An oscillator of two lumped masses linked through a vertical spring moves forward in the horizontal direction, initially at a certain height, over a horizontal Euler beam and descends on it due to its own weight. Vibration of the beam and the oscillator is excited at the onset of the ensuing impact. The impact produced by the descending oscillator is assumed to be either perfectly elastic or perfectly plastic. If the impact is perfectly elastic, the oscillator bounces off and hits the beam a number of times as it moves forward in the longitudinal direction of the beam, exchanging its dynamics with that of the beam. If the impact is perfectly plastic, the oscillator (initially) sticks to the beam after its first impact and then may separate and reattach to the beam as it moves along the beam. Further events of separation and reattachment may follow. This interesting and seemingly simple dynamic problem actually displays rather complicated dynamic behaviour and has never been studied in the past. It is found through simulated numerical examples that multiple events of separation and impact can take place for both perfectly elastic impact and perfectly plastic impact (though more of these in the case of perfectly elastic impact) and the dynamic response of the oscillator and the beam looks noisy when there is an event of impact because impact excites higher-frequency components. For the perfectly plastic impact, the oscillator can experience multiple events of consecutive separation from the beam and subsequent reattachment to it.

• 대한조선학회논문집
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• 제28권2호
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• pp.77-94
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• 1991

일정속도로 항주하는 배에 치하여 생성되는 파를 유한차분법을 이용하여 수치적으로 시뮬레이션 하였다. 지배방정식으로는 3차원 운동량방정식(Euler Eq.)과 연속방정식을 사용하였으며, 직교 좌표 계상에서의 수치계산은 FTCS(forward time/central space)로 차분화하고 시간전진 방법(time marching scheme)으로 수행하였다. 좌표계로 staggered variable mesh system을 채용하여 기존의 계산조직을 개선하므로써, 유체 유동의 변화가 심한 선체주위에 계산 정도를 높이기 위하여 cell을 집중시켰다. 개선된 전산프로그램을 이용하여 Wigley, Series 60($C_{b}$=0.6), 그리고 MS416B 산적화물선 선형등을 대상으로 수치계산을 수행하였으며, 그 결과들을 실험값과 비교하였다.

• Smart Structures and Systems
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• 제12권5호
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• pp.501-521
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• 2013

This paper is concerned with static and dynamic shape control of a laminated Bernoulli-Euler beam hosting a uniformly distributed array of resistively interconnected piezoelectric patches. We present an analytical one-dimensional model for a laminated piezoelectric beam with material discontinuities within the framework of Bernoulli-Euler and extent the model by a network of resistors which are connected to several piezoelectric patch actuators. The voltage of only one piezoelectric patch is prescribed: we answer the question how to design the interconnected resistive electric network in order to annihilate lateral vibrations of a cantilever. As a practical example, a cantilever with eight patch actuators under the influence of a tip-force is studied. It is found that the deflection at eight arbitrary points along the beam axis may be controlled independently, if the local action of the piezoelectric patches is equal in magnitude, but opposite in sign, to the external load. This is achieved by the proper design of the resistive network and a suitable choice of the input voltage signal. The validity of our method is exact in the static case for a Bernoulli-Euler beam, but it also gives satisfactory results at higher frequencies and for transient excitations. As long as a certain non-dimensional parameter, involving the number of the piezoelectric patches, the sum of the resistances in the electric network and the excitation frequency, is small, the proposed shape control method is approximately fulfilled for dynamic load excitations. We evaluate the feasibility of the proposed shape control method with a more refined model, by comparing the results of our one-dimensional calculations based on the extended Bernoulli-Euler equations to three-dimensional electromechanically coupled finite element results in ANSYS 12.0. The results with the simple Bernoulli-Euler model agree well with the three-dimensional finite element results.

• 제어로봇시스템학회논문지
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• 제6권9호
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• pp.836-843
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• 2000

A sequence planning method is proposed to reduce the assembly time of gantey-type chip mounters with single head. The overall path of the chip mounter is divided into forward and backward path, and formulate the optimization problem is formulated as an transpoetation problem and an Euler's tour problem. The transportation alforithm is applied to find optimal backward path, and Euler's tour algorithm used to generate an assembly sequence. Simulation results are presented to verify the usefulness of the proposed method.

• Ocean Science Journal
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• 제40권4호
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• pp.201-208
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• 2005

An accurate particle tracking method for a finite difference method model is developed using a constant acceleration method. Being assumed constant temporal and spatial gradients, the new method permits temporal-spatial variability of particle velocity. Test results in a solid rotating flow show that the new method has second-order accuracy. The performance of the new method is compared with that of other methods; the first-order Euler forward method, and the second-order Euler predictor-corrector method. The new method is the most efficient method among the three. It is more accurate and efficient than the other two.

• 지구물리와물리탐사
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• 제1권2호
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• pp.101-109
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• 1998

항공자력탐사자료를 이용하여 경상분지 동남부 유천소분지의 화산암류 분포지 내에 발달되는 삼량진 칼데라지역에 대한 자력특성을 고찰하였다. 연구방법은 자력탐사 자료를 이용하여 잔여자력도, 자극화변환도, 수평미분도와 수직 2차미분도를 작성하여 자력 암상특성을 분대하고 칼데라구조 및 단층과 관련된 지질구조적 양상에 대한 자력구조 특성을 고찰하는 정성적 해석을 실시하였다. 또한 칼데라 구조를 북동-남서방향으로 종단하는 14.5 km의 단면선에 대해 forward modelling을 실시함과 동시에 전지역에 3-D Euler deconvolution방법을 이용하여 자력 이상체의 심부 발달상태 및 특성을 고찰하는 정량적 해석을 실시하였다. 이들 결과에 의하면 본역의 자력암상특성은 4개의 unit로 분대되며 이들은 일반적으로 본역의 지질분포와 잘 일치되나 삼량진 칼데라 북측 경계부에 관입한 흑운모화강암은 고자력을 보이므로 인접의 여타 저자력 흑운모 화강암체와 자력암상특성에서 분명한 차이를 보인다. 따라서 이 흑운모화강암은 삼량진 칼데라의 화산작용과 밀접한 관계가 있으며 칼데라림을 따라 발달된 구조대를 따라 관입한 것으로 해석된다. 본역의 삼량진 칼데라 구조 및 단층선 구조는 각종 자력 이상도에서 분명한 자력구조로 인지가 가능하며 지형특성도 이들 구조를 잘 반영한다 할 수 있다. 본 역의 심부 자력 이상체 발달상태를 규명하기 위한 자력단면선의 forward modelling결과, 경상퇴적분지의 심도는 칼데라 내에서 평균 약 6 km이며(최고 약 10 km) 칼데라의 외측으로 갈수록 화강암류의 천부 관입에 따라 심도가 얕아짐을 보인다. Euler deconvolution 방법을 이용한 자력이상체의 3차원적 위치 및 심도특성을 고찰한 결과도 칼데라 구조 및 단층구조선을 잘 나타내며 화산암류와 관계된 비교적 천부의 자력 이상체는 주로 동-서와 북동방향으로 발달하고 있음에 반하여 심부의 자력 이상체는 주로 북서 방향으로 발달하고 있음을 알 수 있었다.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2005년도 추계 학술대회논문집
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• pp.261-267
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• 2005

The unsteady flow analysis of staging system is conducted. This study focuses on comparing the results of two different governing equations between Euler equations and Navier-Stokes equations. The Chimera grid scheme is applied to moving simulations for unsteady flow analysis with dynamic simulation. As a result, it is certified that inviscid simulation have capabilities enough to analyze the present staging problem.