• Journal of information and communication convergence engineering
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• 제12권1호
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• 한국안전학회지
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• 제35권3호
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• pp.49-57
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• 2020

In comparison with the existing static reliability analysis methods, the dynamic reliability analysis(DyRA) method is more suitable for estimating the failure probability of a structure subjected to earthquake excitations because it can take into account the frequency characteristics and damping capacity of the structure. However, the DyRA is known to have an issue of numerical stability due to the uncertainty in random sampling of the earthquake excitations. In order to solve this numerical stability issue in the DyRA approach, this study proposed two earthquake-scale factors. The first factor is defined as the ratio of the first earthquake excitation over the maximum value of the remaining excitations, and the second factor is defined as the condition number of the matrix consisting of the earthquake excitations. Then, we have performed parametric studies of two factors on numerical stability of the DyRA method. In illustrative example, it was clearly confirmed that the two factors can be used to verify the numerical stability of the proposed DyRA method. However, there exists a difference between the two factors. The first factor showed some overlapping region between the stable results and the unstable results so that it requires some additional reliability analysis to guarantee the stability of the DyRA method. On the contrary, the second factor clearly distinguished the stable and unstable results of the DyRA method without any overlapping region. Therefore, the second factor can be said to be better than the first factor as the criterion to determine whether or not the proposed DyRA method guarantees its numerical stability. In addition, the accuracy of the numerical analysis results of the proposed DyRA has been verified in comparison with those of the existing first-order reliability method(FORM), Monte Carlo simulation(MCS) method and subset simulation method(SSM). The comparative results confirmed that the proposed DyRA method can provide accurate and reliable estimation of the structural failure probability while maintaining the superior numerical efficiency over the existing methods.

• Structural Engineering and Mechanics
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• 제65권1호
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• pp.91-98
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• Geomechanics and Engineering
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• 제17권6호
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• pp.573-581
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• 2019

Excavation of underground cavern and shaft was proposed for the construction of a ventilation facility in an urban area. A shaft connects the street-level air plenum to an underground cavern, which extends down approximately 46 m below the street surface. At the project site, the rock mass was relatively strong and well-defined joint sets were present. A kinematic block stability analysis was first performed to estimate the required reinforcement system. Then a 3-D discontinuum numerical analysis was conducted to evaluate the capacity of the initial support and the overall stability of the required excavation, followed by a 3-D continuum numerical analysis to complement the calculated result. This paper illustrates the application of detailed numerical analyses to the design of the required initial support system for the stability of underground hard rock mining at a relatively shallow depth.

• Structural Engineering and Mechanics
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• 제83권5호
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• pp.609-615
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• 2022

A numerical approach for dynamic stability analysis of sandwich plates has been provided using Chebyshev-Ritz-Bolotin approach. The sandwich plate with porous core has been formulated according to a higher-order plate. All of material properties are assumed to be dependent of porosity factor which determines the amount or volume of pores. The sandwich plate has also been assumed to be under periodic in-plane loading of compressive type. It will be shown that stability boundaries of the sandwich plate are dependent on static and dynamical load factors, porosity factor, porosity variation and core thickness.

• Earthquakes and Structures
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• 제11권2호
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• pp.297-313
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• 2016

A virtual parameter is introduced into the formulation of the previously published integration method to improve its stability properties. It seems that the numerical properties of this integration method are almost unaffected by this parameter except for the stability property. As a result, it can have second order accuracy, explicit formulation and controllable numerical dissipation in addition to the enhanced stability property. In fact, it can have unconditional stability for the system with the instantaneous degree of nonlinearity less than or equal to the specified value of the virtual parameter for the modes of interest for each time step.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 2010년도 추계 학술발표회 2차
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• pp.186-191
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• 2010

Recently, it has been reported that number of earthquakes was rapidly increased in the Korean Peninsula. According to the interest of seismic analysis, most of construction design must ensure the stability of structure against risks due to earthquake. Therefore, the ground reinforcement and application of seismic standards is necessary and the new structures must secure a stability about Earthquake under the Korea Seismic Analysis Standards. In this study, the 2D numerical analysis was performed to confirm a seismic stability and analysed that behavior of ground and dykes. The numerical seismic response analyses for dykes and its foundation soil were conducted with considering earthquake modes of short-period and long-period, and artificial seismic wave.

• 한국해양공학회지
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• 제27권1호
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• pp.67-73
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• 2013

This paper presents the results of a numerical study on the towing stability of barges. Towing simulations were carried out by using two different numerical models (MMG model and cross-flow model). Stability criteria are also suggested based on the analysis of the linearized governing equations for towed vessel motion. In order to validate the present numerical models, the experimental data of Yasukawa et al. (2006) were used. Simulations were conducted for single and double barges under constant towing speed and direction conditions. The time histories of the heading angle, yaw rate, and towline tension were compared between the numerical results and experiments. The effects of the towline length on the slewing frequency and maximum heading angle were also observed. In addition, a series of numerical simulations using variable hydrodynamic coefficients were performed to investigate the effects of the hydrodynamic forces on the towing stability.

• 산업기술연구
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• 제33권A호
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• pp.73-80
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• 2013

This paper is results of numerical analysis on the behavior of colluvium slope with combinations of soil nails and earth anchors during excavation. In order to maintain the stability of the colluvium cut, being composed of gravel and boulder and thus local in stability being expected during slope cut, temporary reinforcing method of soil nailing with shotcrete might be used. Subsequent method of cast-in-place facing with earth anchors can be used to maintain cut slope stable permanently. For the cut slope where these methods had been applied, the numerical techniques were applied to their behaviors and investigate the stability of the slope. Limit equilibrium methods were used to confirm to maintain the slope stability during and after excavation and application of those reinforcing methods. Another numerical technique of FEM was also used to find the stress and strain as well as deformation distribution in reinforcing materials and slope ground during excavation.

• Geomechanics and Engineering
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• 제38권6호
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• pp.583-591
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• 2024

To properly simulate the excavation process and evaluate the structural stability of the tunnel, rigorous large deformation analysis method is necessary. This study applies two most widely used numerical approaches capable of modelling and considering the large deformations behavior during excavation process to analyze and evaluate the structural stability of circular tunnel based on tunnel boring machine (TBM) excavation. By comparing and combining the results from two numerical approaches, the deformation of the excavated ground will be analyzed. The stability of the circular tunnel from TBM tunneling was assessed based on the maximum deformation occurred during the excavation process. From the numerical computation it was concluded that although the range of the damage on the ground done during excavation was found to be larger under hard rock condition, maximum deformation within the circular tunnel structure was larger under weak ground conditions and deeper tunnel depths.