• Journal of applied mathematics & informatics
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• 제9권1호
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• pp.27-43
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• 2002

Finite element Galerkin solutions for the strongly damped extensible beam equations are considered. The semidiscrete scheme and a fully discrete time Galerkin method are studied and the corresponding stability and error estimates are obtained. Ratios of numerical convergence are given.

• East Asian mathematical journal
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• 제31권5호
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• 드라이브 ㆍ 컨트롤
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• 제21권2호
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• pp.44-52
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• 2024

In this study, we predicted PTO power requirements based on torque predicted by the discrete element method and the multi-body dynamics coupling method. Six different scenarios were simulated to predict PTO power requirements in different soil conditions. The first scenario was a tillage operation on cohesionless soil, and the field was modeled using the Hertz-Mindlin contact model. In the second through sixth scenarios, tillage operations were performed on viscous soils, and the field was represented by the Hertz-Mindlin + JKR model for cohesion. To check the influence of surface energy, a parameter to reproduce cohesion, on the power requirement, a simple regression analysis was performed. The significance and appropriateness of the regression model were checked and found to be acceptable. The study findings are expected to be used in design optimization studies of agricultural machinery by predicting power requirements using the discrete element method and the multi-body dynamics coupling method and analyzing the effect of soil cohesion on the power requirement.

• Advances in Computational Design
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• 제4권1호
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• pp.15-32
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• 2019

One of the efficient and useful tools to achieve the optimal design of structures is employing the sensitivity analysis in the finite element model. In the numerical optimization process, often the semi-analytical method is used for estimation of derivatives of the objective function with respect to design variables. Numerical methods for calculation of sensitivities are susceptible to the step size in design parameters perturbation and this is one of the great disadvantages of these methods. This article uses complex variables method to calculate the sensitivity analysis and combine it with discrete sensitivity analysis. Finally, it provides a new method to obtain the sensitivity analysis for linear structures. The use of complex variables method for sensitivity analysis has several advantages compared to other numerical methods. Implementing the finite element to calculate first derivatives of sensitivity using this method has no complexity and only requires the change in finite element meshing in the imaginary axis. This means that the real value of coordinates does not change. Second, this method has the lower dependency on the step size. In this research, the process of sensitivity analysis calculation using a finite element model based on complex variables is explained for linear problems, and some examples that have known analytical solution are solved. Results obtained by using the presented method in comparison with exact solution and also finite difference method indicate the excellent efficiency of the proposed method, and it can predict the sustainable and accurate results with the several different step sizes, despite low dependence on step size.

• 한국기계기술학회지
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• 제20권6호
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• pp.844-851
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• 2018

In this study, the regression equation was suggested to predict of the shot ball velocity according to blade shapes based on discrete element (DE) analysis. First, the flat type blade DE model was used in the analysis, the validity of the DE model was verified by giving that the velocity of the shot ball almost equal to the theoretical one. Next, the DE analyses for curved and combined blade models was accomplished, and their analytical velocities of shot ball were compared with the theoretical one. The velocity of combined blade model was greatest. From this, the regression equation for velocity of shot ball according to the blade shape based on the DE analysis was derived. Additionally, the wind speed measurement experiment was carried out, and the experimental result and analytical one were the same. Ultimately, it was confirmed that the prediction method of the velocity of shot ball based on DE analysis was effective.

• 한국지반신소재학회논문집
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• 제15권4호
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• pp.33-42
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• 2016

기존 개별요소해석은 암석과 조립재료를 대상으로, 미시거동 분석과 응용을 위한 입상체 역학 및 관련 수치모델의 개발 차원에서 수행되었으나, 시멘트 혼합토(soil-cement)의 본딩 효과를 고려한 분석은 미흡한 것으로 확인되었다. 본 연구에서는 기존의 한계성을 극복하기 위하여 개별요소법 수치모델 프로그램 $PFC^{3D)}$을 이용한 시멘트 혼합토의 본딩 효과 및 실내시험 결과와의 분석을 수행하였다. 시멘트 혼합토에 대한 실내시험은 재령일을 고려한 일축압축강도시험과 시멘트 함유량에 따른 일축압축강도시험을 수행하였으며, 각 실내시험 조건에 적합한 개별요소해석을 수행하였다. 본 연구결과, 개별요소법은 지반공학적 측면에서, 혼합토의 본딩 효과에 대한 미시적 거동(micro behavior) 및 전체적 거동(macro behavior)의 예측뿐아니라, 수치시험실(numerical laboratory)로서 활용될 수 있음을 확인할 수 있었다.

• 터널과지하공간
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• 제30권1호
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• pp.15-28
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• 2020

본 연구는 개별요소법을 이용하여 삼차원 불연속절리망 시스템의 강도 및 변형계수를 추정하기 위해 제안된 기법을 소개하였다. DFN(discrete fracture network) 시스템에서 개별 절리는 유한 길이의 정사각 평면으로 취급하였다. 해석영역은 무결암과 유사한 거동을 하도록 설정된 가상절리와 실제 개별 절리의 조합으로 형성된 다면체로 이산화하였다. 제안된 기법의 적용성을 검토하기 위하여 확정적 및 추계론적 삼차원 DFN 시스템으로 이루어진 한 변이 10m인 정육면체 해석영역에 대하여 개별요소법에 의한 강도 및 변형계수를 추정하는 수치실험이 수행되었다. 또한, 본 연구는 절리의 기하학적 속성이 DFN 시스템의 강도 및 변형 특성에 미치는 영향을 살펴보았다. 제안된 기법은 삼차원 DFN 시스템의 이방적 강도 및 변형 특성을 효과적으로 추정하는 것으로 평가되었다.

• Computers and Concrete
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• 제28권5호
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• pp.521-532
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• 2021

Present paper focuses on the modeling of size effect on the compressive strength of normal concrete with the application of Discrete Element Method (DEM). Test specimens with different size and shape were cast and uniaxial compressive strength test was performed on each sample. Five different concrete mixes were used, all belonging to a different normal strength concrete class (C20/25, C30/37, C35/45, C45/55, and C50/60). The numerical simulations were carried out by using the PFC 5 software, which applies rigid spheres and contacts between them to model the material. DEM modeling of size effect could be advantageous because the development of micro-cracks in the material can be observed and the failure mode can be visualized. The series of experiments were repeated with the model after calibration. The relationship of the parallel bond strength of the contacts and the laboratory compressive strength test was analyzed by aiming to determine a relation between the compressive strength and the bond strength of different sized models. An equation was derived based on Bazant's size effect law to estimate the parallel bond strength of differently sized specimens. The parameters of the equation were optimized based on measurement data using nonlinear least-squares method with SSE (sum of squared errors) objective function. The laboratory test results showed a good agreement with the literature data (compressive strength is decreasing with the increase of the size of the specimen regardless of the shape). The derived estimation models showed strong correlation with the measurement data. The results indicated that the size effect is stronger on concretes with lower strength class due to the higher level of inhomogeneity of the material. It was observed that size effect is more significant on cube specimens than on cylinder samples, which can be caused by the side ratios of the specimens and the size of the purely compressed zone. A limit value for the minimum size of DE model for cubes and cylinder was determined, above which the size effect on compressive strength can be neglected within the investigated size range. The relationship of model size (particle number) and computational time was analyzed and a method to decrease the computational time (number of iterations) of material genesis is proposed.

• 대한수학회지
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• 제59권3호
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• pp.519-548
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• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2007년도 춘계학술대회B
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• pp.3197-3202
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• 2007

An analysis program for pedestrian flow has been developed to investigate the flow patterns of passenger in railway stations. Analysis algorithms for pedestrian flow based on DEM(Discrete Element Method) are newly developed. There are lots of similarity between particle-laden two phase flow and passenger flow. The velocity component of 1st phase corresponds to the unit vector of calculation cell, each particle to passenger, volume fraction to population density and the particle velocity to the walking velocity, etc. And, the walking velocity of passenger is also represented by the function of population density. Key algorithms are developed to determine the position of passenger, population density and numbering to each passenger. By using the developed program, we compared the simulation results of the effects of the location and size of exit and elapsed time.