• 대한기계학회논문집A
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• 제27권11호
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• pp.1907-1916
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• 2003

During decades, there has been much progress in understanding of the inelastic behavior of the materials and numerous inelastic constitutive equations have been developed. The complexity of these constitutive equations generally requires a stable and accurate numerical method. To obtain the increment of state variable, its evolution laws are linearized by several approximation methods, such as general midpoint rule(GMR) or general trapezoidal rule(GTR). In this investigation, semi-implicit integration schemes using GTR and GMR were developed and implemented into ABAQUS by means of UMAT subroutine. The comparison of integration schemes was conducted on the simple tension case, and simple shear case and nonproportional loading case. The fully implicit integration(FI) was the most stable but amplified the truncation error when the nonlinearity of state variable is strong. The semi-implicit integration using GTR gave the most accurate results at tension and shear problem. The numerical solutions with refined time increment were always placed between results of GTR and those of FI. GTR integration with adjusting midpoint parameter can be recommended as the best integration method for viscoplastic equation considering nonlinear kinematic hardening.

• 대한기계학회논문집A
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• 제36권4호
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• pp.437-442
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• 2012

본 논문에서는 효율적인 다물체 시스템의 동역학 해석을 위해 조인트 좌표계 기반의 부분시스템 합성방법을 위한 내재적 적분기법을 개발하였다. 부분시스템 합성방법의 내재적 적분기법을 검증하기 위해, 동일 구조를 갖는 6 개의 독립적인 현가 부분시스템으로 이루어진 무인 로봇 차량에 적용하였다. 내재적 적분기법의 복잡한 시스템 자코비언을 효율적으로 생성하기 위해 기호연산법을 도입하였다. 제안한 방법의 검증을 위해 험지주행 시뮬레이션을 수행하였으며, 일반적인 내재적 적분기법 모델과 그 결과를 비교하였다. 또한 효율성을 확인하기 위해 해석 시간을 비교하였다.

• Structural Engineering and Mechanics
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• 제75권5호
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• pp.541-557
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• 2020

A novel family of controllable, dissipative structure-dependent integration methods is derived from an eigen-based theory, where the concept of the eigenmode can give a solid theoretical basis for the feasibility of this type of integration methods. In fact, the concepts of eigen-decomposition and modal superposition are involved in solving a multiple degree of freedom system. The total solution of a coupled equation of motion consists of each modal solution of the uncoupled equation of motion. Hence, an eigen-dependent integration method is proposed to solve each modal equation of motion and an approximate solution can be yielded via modal superposition with only the first few modes of interest for inertial problems. All the eigen-dependent integration methods combine to form a structure-dependent integration method. Some key assumptions and new techniques are combined to successfully develop this family of integration methods. In addition, this family of integration methods can be either explicitly or implicitly implemented. Except for stability property, both explicit and implicit implementations have almost the same numerical properties. An explicit implementation is more computationally efficient than for an implicit implementation since it can combine unconditional stability and explicit formulation simultaneously. As a result, an explicit implementation is preferred over an implicit implementation. This family of integration methods can have the same numerical properties as those of the WBZ-α method for linear elastic systems. Besides, its stability and accuracy performance for solving nonlinear systems is also almost the same as those of the WBZ-α method. It is evident from numerical experiments that an explicit implementation of this family of integration methods can save many computational efforts when compared to conventional implicit methods, such as the WBZ-α method.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1995년도 추계학술대회 논문집
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• pp.497-500
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• 1995

In this paper, a program for real time simulation of a vehicle is developed. The program uses relative coordinates and BEF(Backward Difference Formula) numerical integration method. Numerical tests showed that the proposed implicit method is more stable in carring out the numerical integration for vehicl dynamics than the explicit method. Hardware requirements for real time simulation are suggested. Algorithms of parallel processing is developed with DSP (digital signal processor).

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2000년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Spring
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• pp.151-158
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• 2000

The use of unconditionally stable implicit time integration techniques for pseudo-dynamic tests has been recently proposed and advanced by several researchers such as Thewalt and Mahin Nakashima and Shing. The developed implicit algorithms are based on a-Method of Hugest et al. In this paper a concise summary and explanation of implicit method for Pseudo dynamic test is presented. Especially The a-C method developed by shing at al. has been in-depth evaluated for this study. Important parameters of the a-C method have been analyzed by the simulation test.

• 한국전산유체공학회지
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• 제16권4호
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• pp.72-83
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• 2011

A high-order discontinuous Galerkin method for the two-dimensional compressible Navier-Stokes equations was developed on unstructured triangular meshes. For this purpose, the BR2 methd(the second Bassi and Rebay discretization) was adopted for space discretization and an implicit Euler backward method was used for time integration. Numerical tests were conducted to estimate the convergence order of the numerical solutions of the Poiseuille flow for which analytic solutions are available for comparison. Also, the flows around a flat plate, a 2-D circular cylinder, and an NACA0012 airfoil were numerically simulated. The numerical results showed that the present implicit discontinuous Galerkin method is an efficient method to obtain very accurate numerical solutions of the compressible Navier-Stokes equations on unstructured meshes.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.549-570
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• 2008

Numerical integration is an efficient approach for nonlinear dynamic analysis. In this paper, general category of the implicit integration errors will be discussed. In order to decrease the errors, Dynamic Relaxation method with modified time step (MFT) will be used. This procedure leads to an alternative algorithm which is very general and can be utilized with any implicit integration scheme. For numerical verification of the proposed technique, some single and multi degrees of freedom nonlinear dynamic systems will be analyzed. Moreover, results are compared with both exact and other available solutions. Suitable accuracy, high efficiency, simplicity, vector operations and automatic procedures are the main merits of the new algorithm in solving nonlinear dynamic problems.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2000년도 봄 학술발표회 논문집
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• pp.617-622
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• 2000

The use of unconditionally stable implicit time integration techniques for pseudo-dynamic test has been recently proposed and advanced by several researchers such as Thewalt and Mahin, Nakashima and Shing, etc. The developed implicit algorithms are based on the $\alpha$-Method of Huges et al. In this paper, a concise summary and explanation of implicit method for Pseudo dynamic tese is presented. Especially, The $\alpha$-C method developed by shing et al. has been in-depth evaluated for this study. Important parameters of the $\alpha$-C method have been analyzed by the simulation test.

• 한국항공우주학회지
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• 제31권7호
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• pp.1-8
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• 2003

본 논문은 극초음속 유동과 공력가열 해석에서 나타나는 공기 반응의 수치해석적 특징을 다루고 공기반응을 효율적으로 해석하는 부분 내재적 적분법을 공기반응에 적용하였다. 안정적 계산을 위해 화학반응 자코비안이 필수적임을 밝혔으며 자코비안의 양의 실수 특성치로 인한 수치기법의 경직성은 일반적인 연소반응에 비하여 미약하였다. 공기반응에서 부분 내재적 적분법은 화학종 순서의 종속성이 없었으며 완전 내재적 적분법과 동일한 수렴율과 계산 결과를 보였다. 극초음속 유동해석에 부분 내재적 적분법을 적용하면 전체 연산 시간이 감소되었다.

• Wind and Structures
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• 제34권1호
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• pp.59-72
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• 2022

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).