• Journal of the Earthquake Engineering Society of Korea
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• v.2 no.3
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• pp.27-35
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• 1998

Steel structures with added viscoelastic dampers are analysed to investigat their behavior under earthquake excitation. The direct integration method, which produces exact solution for the non-proportional or non-classical damping system, is used throughout the analysis. The results from modal strain energy method are also provided for comparison. Then a new analytical a, pp.oach, based on the rigid floor diaphragm assumption and matrix condensation technique, is introduced, and the results are compared with those obtained from direct integration method and modal strain energy method. The well known phenomenon, that the effectiveness of the viscoelastic dampers depends greatly on the location of the dampers, is once again confirmed in the analysis. It is also found that the modal strain energy method generaly underestimates the responses obtained from the direct integration method, especially when the dampers are placed in only a part of the building. The proposed method turns out to be very efficient with considerable saving in computation this and reasonably accurate considering the reduced degrees of freedom.

• 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.

• 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.

• 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.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.7 no.3
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• pp.241-248
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• 1987

The theoretical backgrounds of the several methods were surveyed and reviewed to fin out the adequate one to determine equivalent modal damping values in solving the dynamic problem of soil-structure interaction by mode superposition method. Furthermore the rigorous damping matrix of equation of motion was obtained through component mode synthesis technique and used in direct integration of the equation. The analytical results by direct integration method were compared with those of mode superposition approach using the various sets of equivalent modal damping values calculated by the methods to be reviewed. Two types of superstructures and four kinds of subsurface conditions were considered and combined to make soil-structure coupled models. It was realized that dissipating energy method gives the equivalent modal damping values which lead the most similar results to direct integration ones. In case of fixed base, the responses of all methods except stiffness weighted approach are almost equal to those of direct integration method.

• Geosystem Engineering
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• v.21 no.6
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• pp.309-317
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• 2018

We employ a three-dimensional indirect boundary element method (BEM) to simulate temperature change around an underground liquefied natural gas storage cavern. The indirect BEM (IBEM) uses fictitious heat source strength on boundary elements as basic variables which are solved from equations of boundary conditions and then used to compute the temperature change at other points in the considered problem domain. The IBEM requires evaluation of singular integration for temperature change due to heat conduction from a constant heat source on a planar (triangular) region. The singularity can be eliminated by a semi-analytical integration scheme. However, it is found that the semi-analytical integration scheme yields sharp temperature gradient for points close to vertices of triangle. This affects the accuracy of heat flux, if they are evaluated by finite difference method at these points. This difficulty can be overcome by a combination of using a direct numerical integration for these points and the semi-analytical scheme for other points distance away from the vertices. The IBEM and the hybrid integration scheme have been verified with an analytic solution and then used to the application of the underground storage.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.04a
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• pp.37-44
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• 1993

There are a lot of linear dynamic analysis methods for complex structures. Each method has advantages and shortcomings. Method of dynamic analysis for complex structure is selected considering characteristics of dynamic loading, computer facility available number of degree of freedem and accuracy of results. It is a main point of view to get economical results rather then accurate ones for analysis of general complex structures, Mode superposition method and direct integration method are generally used. However, the characteristics of load is not considered in mode superpositon method, the personal computer cannot be used in direct integration methods. To over-come these shortcomings, the component mode method incorporating Ritz algorithm updated is proposed to solve economically dynamic behavior of the structures. The purpose of study is a formulation of algorithm, and computer programing suitable for dynamic analysis of the complex structure in personal computer environment.

• Structural Engineering and Mechanics
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• v.17 no.6
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• pp.735-749
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• 2004

This work presents a direct integration scheme, based on a fourth order finite difference approach, for elastodynamics. The proposed scheme was chosen as an alternative for attenuating the errors due to the use of the central difference method, mainly when the time-step length approaches the critical time-step. In addition to eliminating the spurious numerical oscillations, the fourth order finite difference scheme keeps the advantages of the central difference method: reduced computer storage and no requirement of factorisation of the effective stiffness matrix in the step-by-step solution. A study concerning the stability of the fourth order finite difference scheme is presented. The Finite Element Method and the Boundary Element Method are employed to solve elastodynamic problems. In order to verify the accuracy of the proposed scheme, two examples are presented and discussed at the end of this work.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.885-900
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• 2015

This paper introduces Romberg-Richardson's method as one of the numerical integration tools for computation of stress intensity factor in a pre-cracked specimen subjected to a complex stress field across the crack faces. Also, the computation of stress intensity factor for various stress fields using existing three methods: average stress over interval method, piecewise linear stress method, piecewise quadratic method are modified by using Richardson extrapolation method. The direct integration method is used as reference for constant and linear stress distribution across the crack faces while Gauss-Chebyshev method is used as reference for nonlinear distribution of stress across the crack faces in order to obtain the stress intensity factor. It is found that modified methods (average stress over intervals-Richardson method, piecewise linear stress-Richardson method, piecewise quadratic-Richardson method) yield more accurate results after a few numbers of iterations than those obtained using these methods in their original form. Romberg-Richardson's method is proven to be more efficient and accurate than Gauss-Chebyshev method for complex stress field.