• 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.

• Proceedings of the Korean Geotechical Society Conference
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• 1995.10a
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• pp.15.2-22
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• 1995

Evaluating stiffness of near-surface materials has been one of the critically important tasks in many civil engineering works. It is the main goal of geotechnical characterization. The so-called deflection-response method evaluates the stiffness by measuring stress-strain behavior of the materials caused by static or dynamic load. This method, however, evaluates the overall stiffness and the stiffness variation with depth cannot be obtained. Furthermore, evaluation of a large-area geotechnical site by this method can be time-consuming, expensive, and damaging to many surface points of the site. Wave-propagation method, on the other hand, measures seismic velocities at different depths and stiffness profile (stiffness change with depth) can be obtained from the measured velocity data. The stiffness profile is often expressed by shear-wave (S-wave) velocity change with depth because S-wave velocity is proportional to the shear modulus. that is a direct indicator of stiffiiess. The crosshole and downhole method measures the seismic velocity by placing sources and receivers (geophones) at different depths in a borehole. Requirement of borehole installation makes this method also time-consuming, expensive, and damaging to the sites. Spectral-Analysis-of-Surface-Waves (SASW) method places both source and receivers at the surface, and records horizontally-propagating surface waves. Based upon the theory of surfacewave dispersion, the seismic velocities at different depths are calculated by analyzing the recorded surface-wave data. This method can be nondestructive to the sites. However, because only two receivers are used, the method requires multiple measurements with different field setups and, therefore, the method often becomes time-consuming and labor-intensive. Furthermore. the inclusion of noise wavefields cannot be handled properly, and this may cause the results by this method inaccurate. When multi-channel recording method is employed during the measurement of surface-waves, there are several benefits. First, usually single measurement is enough because multiple number (twelve or more) of receivers are used. Second, noise inclusion can be detected by coherency checking on the multi-channel data and handled properly so that it does not decrease the accuracy of the result. Third, various kinds of multi-channel processing techniques can be applied to f1lter unwanted noise wavefields and also to analyze the surface-wavefields more accurately and efficiently. In this way, the accuracy of the result by the method can be significantly improved. Fourth, the entire system of source, receivers, and recording-processing device can be tied into one unit, and the unit can be pulled by a small vehicle, making the survey speed very fast. In all these senses, multi-channel recording of surface waves is best suited for a routine method for geotechnical characterization in most of civil engineering works.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.13 no.2
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• pp.99-107
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• 2003

The finite element method(FEM) is the most widely used and powerful method for structural analysis. In general, in order to analyze complex and large structures, we have used the FEM. However, it is necessary to use a large amount of computer memory and computation time for solving accurately by the FEM the dynamic problem of a system with many degree-of-freedom, because the FEM has to deal with very large matrices in this case. Therefore, it was very difficult to analyze the vibration for plate structures with a large number of degrees of freedom by the FEM on a personal computer. For overcoming this disadvantage of the FEM without the loss of the accuracy, the finite element-transfer stiffness coefficient method(FE-TSCM) was developed. The concept of the FE-TSCM is based on the combination of modeling technique in the FEM and the transfer technique in the transfer stiffness coefficient method(TSCM). The merit of the FE-TSCM is to take the advantages of both methods, that is, the convenience of the modeling in the FEM and the computation efficiency of the TSCM. In this paper, the forced vibration analysis algorithm of plate structures is formulated by the FE-TSCM. In order to illustrate the accuracy and the efficiency of the FE-TSCM, results of frequency response analysis for a rectangular plate, which was adopted as a computational model, were compared with those by the modal analysis method and the direct analysis method which are based on the FEM.

• Journal of the Earthquake Engineering Society of Korea
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• v.3 no.2
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• pp.87-96
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• 1999

To analyze the dynamic behavior of structure, direct integration and mode superposition may be utilized in time domain analysis. As finite number of frequencies can give relatively exact solutions, mode superposition is preferable in analyzing structural behavior. In non-linear analysis, however, mode superposition is seldom used since time-varying element stiffness changes stiffness matrix, and the change of stiffness matrix leads to the change of essential constants - natural frequencies and mode shapes. In spite of these difficulties, there are some attempts to adopt mode superposition because of low cost compared to direct integration, but the result is not satisfactory. In this paper, a method using mode superposition in non-linear analysis is presented by separating local element stiffness from global stiffness matrix with the difference between linear and non-linear restoring forces to the external force vectors included. Moreover, the hysteresis model changing with the relative deformation in each floor makes it possible to analyze non-linear behavior of structure. The proposed algorithm is applied to shear beam model and the maximum displacement is compared with the result using direct integration method.

• Journal of Navigation and Port Research
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• v.30 no.2
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• pp.137-143
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• 2006

The optimum grillage design belongs to nonlinear constrained optimization problem. The determination of beam scantlings for the grillage structure is a very crucial matter out of whole structural design process. The performance of optimization methods, based on penalty functions, is highly problem-dependent and many methods require additional tuning of some variables. This additional tuning is the influences of penalty coefficient, which depend strongly on the degree of constraint violation. Moreover, Binary-coded Genetic Algorithm (BGA) meets certain difficulties when dealing with continuous and/or discrete search spaces with large dimensions. With the above reasons, Real-coded Micro-Genetic Algorithm ($R{\mu}GA$) is proposed to find the optimum beam scantlings of the grillage structure without handling any of penalty functions. $R{\mu}GA$ can help in avoiding the premature convergence and search for global solution-spaces, because of its wide spread applicability, global perspective and inherent parallelism. Direct stiffness method is used as a numerical tool for the grillage analysis. In optimization study to find minimum weight, sensitivity study is carried out with varying beam configurations. From the simulation results, it has been concluded that the proposed $R{\mu}GA$ is an effective optimization tool for solving continuous and/or discrete nonlinear real-world optimization problems.

• Tunnel and Underground Space
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• v.5 no.1
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• pp.1-10
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• 1995

The behavior of a jointed rock mass depends mainly on the geometrical and mechanical properties of joints. The failure mode of a rock mass and kinematics of rock blocks are governed by the orientation, spacing, and persistence of joints. The mechanical properties such as dilation angle, shear strength, maximum closure, strength of asperities and friction coeffiient play important roles on the stability and deformation of the rock mass. The normal and shear behaviour of a joint are coupled due to dilation, and the joint deformation depends also on the boundary conditions such as stiffness conditons. In this paper, the joint constitutive law including the dilatant behaviour of a joint is numerically modelled using the edge-to-edge contact logic in distinct element method. Also, presented is the method to quantify the input parameters used in the joint law. The results from uniaxial compression and direct shear tests using the numeical model of the single joint were compared to the analytic results from them. The boundary effect on the behaviour of a joint is verified by comparing the results of direct shear test under constant stress boundary condition with those under constant stiffness boundary condition. The numerical model developed is applied to a complex jointed rock mass to examine its performance and to evaluate the effect of joint dilation on tunnel stability.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.193-199
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• 2001

Active control of forced vibration of the cantilevered laminated composite plates using collocated piezoceramic sensor/actuator is analyzed numerically and verified experimentally for various fiber orientations. Impact on the stiffness and the damping properties is studied by varying stacking sequence of [$\theta$$_{4}$O$_{2}$90$_{2}$]s for the laminated composite plate. For the forced vibration control, the plate is excited by one pair of collocated PZT exciters in resonance and its vibrational response is suppressed by the other collocated PZT sensor/actuator using direct negative velocity feedback. It is shown that the active control of forced vibration is more effective for the smart laminated plate with higher modal damped stiffness(2ζ$\omega$/aup 2/) .

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2002.09a
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• pp.258-265
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• 2002

Most structures are expected deform nonlinear and inelastic behavior when subjected to strong ground motion. Nonlinear time history analysis(NTHA) is the most rigorous procedure to compute seismic performance in the various inelastic analysis methods. But nonlinear analysis procedures necessitate more reliable and practical tools for predicting seismic behavior of structures. Some building codes propose the capacity spectrum method. This method is the concept of an equivalent linear system, wherein a linear system having reduced stiffness and increased damping is used to estimate the response of the nonlinear system. This procedure are conceptually simple, but the iterative procedure is time-consuming and may sometimes lead to no solution or multiple solutions. This paper presents a nonlinear direct spectrum method(NDSM) to evaluate seismic performance of structures, without iterative computations, given by the structural initial elastic period and yield strength from the pushover analysis, especially for mixed building structure.

• 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.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.53-60
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• 2002

It has been recognized that damage control must become a more explicit design consideration. In an effort to develop design methods based on performance it is clear that the evaluation of the inelastic response is required. The methods available to the design engineer today are nonlinear time history analyses, or monotonic static nonlinear analyses, or equivalent static analyses with simulated inelastic influences. Some codes proposed the capacity spectrum method based on the nonlinear static(pushover) analysis to determine earthquake-induced demand given the structure pushover curve. This procedure is conceptually simple but iterative and time consuming with some errors. This paper presents a nonlinear direct spectrum method to evaluate seismic Performance of structure, without iterative computations, given the structural initial elastic period and yield strength from the pushover analysis, especially for multi degree of freedom structures. The purpose of this paper is to investigate accuracy and confidence of this method from a point of view of various earthquakes and unloading stiffness degradation parameters.