• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.374-381
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• 1995

In this paper, integration methods for stiff constrained mechanical systems are studied to analyze dynamic response of the stiff mechanical system efficiently. The stiff, non-stiff systems are identified by using eigenvalues of the Jacobian of the systems. To integrate both stiff system and non-stiff system efficiently a new switching method between the non-stiff differential equation solver and the stiff differential equation solver is presented.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.165-180
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• 2017

In this study, Taylor matrix algorithm is designed for the approximate solution of linear and non-linear differential equation systems. The algorithm is essentially based on the expansion of the functions in differential equation systems to Taylor series and substituting the matrix forms of these expansions into the given equation systems. Using the Mathematica program, the matrix equations are solved and the unknown Taylor coefficients are found approximately. The presented numerical approach is discussed on samples from various linear and non-linear differential equation systems as well as stiff systems. The computational data are then compared with those of some earlier numerical or exact results. As a result, this comparison demonstrates that the proposed method is accurate and reliable.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.224-261
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• 2021

The interest in implicit-explicit (IMEX) integration methods has emerged as an alternative for dealing in a computationally cost-effective way with stiff ordinary differential equations arising from practical modeling problems. In this paper, we introduce implicit-explicit second derivative linear multi-step methods (IMEX SDLMM) with error control. The proposed IMEX SDLMM is based on second derivative backward differentiation formulas (SDBDF) and recursive SDBDF. The IMEX second derivative schemes are constructed with order p ranging from p = 1 to 8. The methods are numerically validated on well-known stiff equations.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.212-215
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• 1986

For distillation columns, dynamic models which consider variable pressure and vapor holdup were studied. A most rigorous model which used the vapor hydraulic equation was studied with implicit methods. Vapor holdup must be considered in high pressure columns in order to predict dynamic responses accurately. The effect of pressure changes on the tray was only important for the vacuum column, particularly when heat input disturbances occurred. The rigorous vapor hydraulic model was shown to be useful, despite the fact that it is extremely stiff, provided an implicit integration algorithm (LSODES) is employed.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• Structural Engineering and Mechanics
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• v.39 no.5
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• pp.683-701
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• 2011

In this study, inelastic displacement ratios and ductility demands are investigated for SDOF systems with period range of 0.1-3.0 s. with elastoplastic behavior considering soil structure interaction. Earthquake motions recorded on different site conditions such as rock, stiff soil, soft soil and very soft soil are used in analyses. Soil structure interacting systems are modeled with effective period, effective damping and effective ductility values differing from fixed-base case. For inelastic time history analyses, Newmark method for step by step time integration was adapted in an in-house computer program. Results are compared with those calculated for fixed-base case. A new equation is proposed for inelastic displacement ratio of interacting system ($\tilde{C}_R$) as a function of structural period of interacting system ($\tilde{T}$), strength reduction factor (R) and period lengthening ratio ($\tilde{T}/T$). The proposed equation for $\tilde{C}_R$ which takes the soil-structure interaction into account should be useful in estimating the inelastic deformation of existing structures with known lateral strength.

• Steel and Composite Structures
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• v.32 no.2
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• pp.253-264
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• 2019

This paper presents the combination resonances of FG porous (FGP) cylindrical shell under two-term excitation. The effect of structural damping on the system response is also considered. With regard to classical plate theory of shells, von-$K{\acute{a}}rm{\acute{a}}n$ equation and Hook law, the relations of stress-strain is derived for shell. According to the Galerkin method, the discretized motion equation is obtained. The combination resonances are obtained by using the method of multiple scales. Four types of FGP distributions consist of uniform porosity, non-symmetric porosity soft, non-symmetric porosity stiff and symmetric porosity distribution are considered. The influence of various porosity distributions, porosity coefficients of cylindrical shell and amplitude excitations on the combination resonances for FGP cylindrical shells is investigated.

• Coupled systems mechanics
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• v.12 no.6
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• pp.519-530
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• 2023

This paper presents a mathematical model suitable for the calculation of laminated glass, i.e. glass plates combined with an interlayer material. The model is based on a beam differential equation for each glass plate and a separate differential equation for the slip in the interlayer. In addition to slip, the model takes into account prestressing force in the interlayer. It is possible to combine the two contributions arbitrarily, which is important because the glass sheet fabrication process changes the stiffness of the interlayer in ways that are not easily predictable and could introduce prestressing of varying magnitude. The model is suitable for reformulation into an inverse procedure for calculation of the relevant parameters. Model consisting of a system of differential-algebraic equations, proved too stiff for cases with the thin interlayer. This novel approach covers the full range of possible stiffnesses of layered glass sheets, i.e., from zero to infinite stiffness of the interlayer. The comparison of numerical and experimental results contributes to the validation of the model.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.617-624
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• 2002

An equation of J-integral for a penny-shaped crack at the end of the fiber embedded in rubber matrix is proposed. The values of J-integral for the specimens with various crack and specimen radius are obtained by FEA(Finite Element Analysis). The dimensional analysis is applied to derive an equation of J-integral as a nonlinear elastic energy release rate. The geometry and deformation calibration function in an equation of J can be expressed in a separated form. The geometry calibration function characterizing the effects of cord and specimen size is expressed in a polynomial form of fourth order. The deformation calibration function characterizes the effect of the overall level of strain. As approaching the infinitesimal strain, the value of the deformation calibration function approaches the results of LEFM(Linear Elastic Fracture Mechanics).

• Journal of the Korea institute for structural maintenance and inspection
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• v.18 no.3
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• pp.84-92
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• 2014

In this study, vibrational tendon tension measurement methods are applied to estimate tension of external tendons used in segmental post-tensioned bridges. The acceleration of various length type of tendons is measured and natural frequencies are obtained using FFT (Fast Fourier Transform). The obtained natural frequencies are within 1% error regardless of sensor direction and location. On the basis of natural frequency of tendon, estimation of the tendon tension is performed by using many types of solutions such as string theory equation, multi mode estimation, practical formula estimation and stiff string with clamped-clamped boundary conditions. The results are compared with each other and have shown that the flexural stiffness is not negligible in tendons of this type causing the vibration mode to be inharmonically related. The results have shown that the method using stiff string equation with clamped-clamped boundary conditions is more accurate than the other methods. Application example of in-service bridges has shown that force distribution effects from friction at deviation blocks can be effectively detected.