• Computational Structural Engineering
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• v.9 no.3
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• pp.187-197
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• 1996

An explicit direct time integration method based solution algorithm is presented to predict dynamic buckling response of Euler column. On the basis of large deflection beam theory, a plane frame finite element is formulated and implemented into the solution algorithm. The element formulation takes into account geometrical nonlinearity and overall buckling of steel structural frames. The solution algorithm employs the central difference method. Using the computer program developed by the author, dynamic instability behavior of Euler column under impact loading is investigated by considering the time variation of load, load magnitude, and load duration. The free vibration of Euler column caused by a short duration impact load is also studied. The validity and efficiency of the present formulation and solution algorithm are verified through illustrative numerical examples.

• Journal of the Korea institute for structural maintenance and inspection
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• v.6 no.3
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• pp.139-149
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• 2002

An explicit direct time integration method based solution algorithm is proposed to predict dynamic postbuckling response of thin plates. Based on the von Karman's plate equations and Marquerre's shallow shell theory, a rectangular plate finite element is formulated and utilized in this study. The element formulation takes into account geometrical nonlinearity and initial deflection of plates. The solution algorithm employs the central difference method. Using the computer program developed by the authors, dynamic postbuckling behavior of elastic thin plates under impact loading is investigated by considering the time variation of load and load duration. The efficiency of the proposed solution algorithm is examined through illustrative numerical examples.

• Structural Engineering and Mechanics
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• v.4 no.6
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• pp.589-600
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• 1996

An explicit 4th order time integration scheme for solving the convection-diffusion equation is discussed in this paper. A system of ordinary differential equations are derived first by discretizing the spatial derivatives of the relevant PDE using the finite difference method. The integration of the ODEs is then carried out using a 4th order scheme and a self-adaptive technique based on the spatial grid spacing. For a non-uniform spatial grid, different time step sizes are used for the integration of the ODEs defined at different spatial points, which improves the computational efficiency significantly. A numerical example is also discussed in the paper to demonstrate the implementation and effectiveness of the method.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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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).

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.311-327
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• 2016

In this paper, we propose an error embedded Runge-Kutta method to improve the traditional embedded Runge-Kutta method. The proposed scheme can be applied into most explicit embedded Runge-Kutta methods. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. These solution and error are obtained by solving an initial value problem whose solution has the information of the error at each integration step. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. For the assessment of the effectiveness, the van der Pol equation and another one having a difficulty for the global error control are numerically solved. Finally, a two-body Kepler problem is also used to assess the efficiency of the proposed algorithm.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2000.10a
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• pp.136-140
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• 2000

It is desirable to predict springback quantitatively and accurately for the tool and process design in sheet stamping operations, however, it is blown very difficult. The result of springback analysis by the finite element method is sensitively influenced by numerical factors such as blank element size, number of integration point, punch velocity, contact algorithm etc. In the present work, a parametric study by Taguchi method is performed in order to evaluate the influence of numerical factors on springback Quantitatively and to obtain the combination of numerical factors which yields the best approximation to experimental data. Since springback is determined by the residual stress after forming process, it is important to evaluate stress distribution accurately. The oscillation in the time history curve of stress obtained by explicit FEM says that the stress solution at termination time is in very unstable state. Therefore, a variability study is also carried out in this study in order to assess the stability of implicit springback analysis starting from the stress solution by explicit forming simulation. The 2D draw bending process, one of the NUMISHEET '93 benchmark problems, is adopted as an application model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.93-102
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• 2020

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1551-1562
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• 1991

최근까지 발표된 유한 요소법을 이용한 압연 해석 관련 주요 논문들을 정리해 보면 다음과 같다. Li와 Kobayashil는 강소성 유한 요소법(rigidplastic finite element method)을 여러가지 마찰조건에 대하여 해석하였다. 이때 압연롤은 강체 (rigid body)로 시편은 가공경화(workhardening)를 동반한 강소성체로 모델링하였다. Hwang과 Kobayashi는 강소성 유한 요소법을 이용한 평면 변형 압연에서 재료 손실을 최소화하는 예비 성형체(preform)의 설계에 대한 연구를 수행하였다. 이 경우에도 역시 압연롤은 강체로 시편은 가공 경화를 동반한 강소성체와 완전 소성체로 모델링 되었으나, 고착(sticking) 마찰 조건에 대해서만 해석을 수행하였다. Mori와 Osak- ada 그리고 Oda는 약간 압축성이 있는 재료의 평면 변형 압연에 대하여 연구하였다. 이때 압연롤은 강체로 시편은 가공 경화를 동반한 강소성체로 모델링 되었으며 경계 면에서는 Coulomb 마찰을 고려하였다. 이밖에도 오일러(Eulerian) 수식화를 이용한 Dawson과 Thompson, Berman의 해석 결과가 있으며, 또 폭 방향의 변형까지를 고려한 Li와 Kobayashi, Mori와 Osakada의 3차원 해석 결과가 있다.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.497-502
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• 2004

This paper presents applications of the objective stress rates to stress update algorithms for transient shell dynamic analysis within the context of explicit time integration. The hypo elasto-plastic materials are assumed in establishing constitutive equations. The derivation of the objective stress rates are investigated by use of the Lie derivative. Comparison results are given between the Kirchhoff and Cauchy stress formulation. The Jacobian determination algorithm proposed in this paper is presented in association with the Belytschko-Lin-Tsay shell theory. Several numerical examples are demonstrated including contact and non-contact examples, by which proposed algorithms are compared with respect to the accuracy and effectiveness.