• 한국기계연구소 소보
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• s.18
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• pp.55-66
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• 1988

Many direct integration methods are used for numerical analyses of dynamic motion. In these methods, the governing equations of a dynamic system are integrated successively using a step-by-step numerical integration procedure. Time derivatives in the equations are generally approximated using difference formulas involving one or more increments of the time. Time increment has closely relationship with the accuracy of the motion analysis. In this paper, a 4th order Houbolt direct integration method is derived. For a spring-mass system, the motion of the system are analyzed from the 3rd order Houbolt and the 4th order Houbolt approaches respectively. Finally the paper proposes the optimal time-increment based on the accuracy of numerical analyses.

• Structural Engineering and Mechanics
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• v.13 no.5
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• pp.569-589
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• 2002

In performing the dynamic analysis, the step size used in a step-by-step integration method might be much smaller than that required by the accuracy consideration in order to capture the rapid chances of dynamic loading or to eliminate the linearization errors. It was first found by Chen and Robinson that these difficulties might be overcome by integrating the equations of motion with respect to time once. A further study of this technique is conducted herein. This include the theoretical evaluation and comparison of the capability to capture the rapid changes of dynamic loading if using the constant average acceleration method and its integral form and the exploration of the superiority of the time integration to reduce the linearization error. In addition, its advantage in the solution of the impact problems or the wave propagation problems is also numerically demonstrated. It seems that this time integration technique can be applicable to all the currently available direct integration methods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.8
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• pp.826-832
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• 2007

Fully flexible cell preserves Hamiltonian in structure so that the symplectic time integrator is applicable to the equations of motion. In the direct formulation of fully flexible cell N-Sigma-T ensemble, a generalized leapfrog time integration (GLF) is applicable for fully flexible cell simulation, but the equations of motion by GLF has structure of implicit algorithm. In this paper, the time integration formula is derived for the fully flexible cell molecular dynamics simulation by using the splitting time integration. It separates flexible cell Hamiltonian into terms corresponding to each of Hamiltonian term. Thus the simple and completely explicit recursion formula was obtained. We compare the performance and the result of present splitting time integration with those of the implicit generalized leapfrog time integration.

• Structural Engineering and Mechanics
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• v.16 no.2
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• pp.219-240
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• 2003

One of the most versatile approaches for analyzing the dynamic behavior of structural systems is direct time integration of semi-discrete equations of motion. However responses computed by time integration are generally inexact and hence the corresponding errors would rather be studied in advance. In spite of the various error estimation formulations that exist in the literature, it is accepted practice to repeat the analyses with smaller time steps, followed by a comparison between the results. In this paper, after a review of this simple method and disregarding the round-off errors, a more efficient, reliable and yet simple method for estimating errors and enhancing the accuracy is proposed. The main objectives of this research are more realistic error estimation based on the concept of convergence, approximately controlling the reliability by comparing the actual rate of convergence with the integration method's order of accuracy, and enhancement of reliability by applying Richardson's extrapolation. Starting from the errors at specific time instants, the study is then generalized to cases in which the errors should be estimated and decreased at specific events e.g. peak responses. Numerical study illustrates the efficacy of the proposed method.

• Structural Engineering and Mechanics
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• v.64 no.4
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• pp.495-504
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• 2017

This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method's degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.1
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• pp.48-53
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• 2000

The novel integration method with programmable high-pass filter is suggested in order to solve the problem of integration for stator flux estimation in a stator flux oriented direct vector controlled induction motor drive system. The dc offset in a pure integrator is eliminated using high-pass filter with fixed time constant, and then time constant of programmable high-pass filter is controlled with a inverter frequency for integration in a wide frequency range, considering phase lag and attenuation due to both the hardware low-pass filter and high-pass filter. The proposed method is verified with the experimental results implemented by 32-bit DSP.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.9
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• pp.674-684
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• 2002

In order to decrease remarkably the computation time and storage used in the direct integration method without the loss of accuracy, authors suggest a new transient analysis algorithm. This algorithm is derived from the combination of three techniques, that is, the transfer technique of the transfer stiffness coefficient method, the modeling technique of the finite element method, and the numerical integration technique of the Newmark method. In this paper, the transient analysis algorithm of a frame structure is formulated by the proposed method. The accuracy and computation efficiency of the proposed method are demonstrated through the comparing with the computation results by the direct integration method for three computation models under various excitations.

• Proceedings of the KSME Conference
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• 2001.06c
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• pp.402-407
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• 2001

Sensitivity analysis scheme is developed in the elasto-plastic finite element method with explicit time integration using direct differentiation method. The direct differentiation is concerned with the time integration, constitutive relation, shell element with reduced integration and the contact scheme. Sensitivity analysis results are mainly examined with the highly nonlinear and quasi-static problem with the complicated contact condition. The result shows stable sensitivity especially in the sheet metal forming analysis.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 1999.10a
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• pp.155-161
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• 1999

Many direct integration methods have been developed for dynamic analysis of structures, In order to compare each other methods and give guideline for selecting a time increment the amplification matrix is constructed according to algorithm of each method and stability and accuracy analysis is done. Four story shear building under external excitations is analyzed by each method and the RMS errors of displacements of top floor and compared with each other.

• Bulletin of the Society of Naval Architects of Korea
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• v.22 no.2
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• pp.27-34
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• 1985

In this paper, the second order time mean forces acting on the circular cylinder floating on the free surface of a finite water depth are calculated. Under the assumption that fluid is idea and the wave the linear gravity wave, the velocity potential is calculated by the source distribution method, and the second order time mean lateral and vertical drifting forces are calculated by the direct integration of fluid pressures over the immersed body surface. The comparison of the lateral drifting forces with Rhee's results by momentum theorem shows good agreements. And it is shown that the second order time sinkage forces of a floating circular cylinder cross zero for all water depths.