• Coupled systems mechanics
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• v.7 no.6
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• pp.669-690
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• 2018

This paper deals with numerical modeling of dynamic failure phenomena in rate-sensitive brittle and/or ductile materials. To this end, a two-dimensional continuum viscodamage-embedded discontinuity model, which is based on our previous work (see Do et al. 2017), is developed. More specifically, the pre-peak nonlinear and rate-sensitive hardening response of the material behavior, representing the fracture-process zone creation, is described by a rate-dependent continuum damage model. Meanwhile, an embedded displacement discontinuity model is used to formulate the post-peak response, involving the macro-crack creation accompanied by exponential softening. The numerical implementation in the context of the finite element method exploiting the second-order mid-point scheme is discussed in detail. In order to show the performance of the model several numerical examples are included.

• Journal of applied mathematics & informatics
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• v.36 no.3_4
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• pp.181-203
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• 2018

In this paper, we have constructed an overlapping Schwarz method for singularly perturbed second order convection-diffusion equations. The method splits the original domain into two overlapping subdomains. A hybrid difference scheme is proposed in which on the boundary layer region we use the central finite difference scheme on a uniform mesh while on the non-layer region we use the mid-point difference scheme on a uniform mesh. It is shown that the numerical approximations which converge in the maximum norm to the exact solution. When appropriate subdomains are used, the numerical approximations generated from the method are shown to be first order convergent. Furthermore it is shown that, two iterations are sufficient to achieve the expected accuracy. Numerical examples are presented to support the theoretical results. The main advantages of this method used with the proposed scheme is it reduces iteration counts very much and easily identifies in which iteration the Schwarz iterate terminates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.29 no.2 s.233
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• pp.253-261
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• 2005

In decades, a substantial body of work on a unified viscoplastic model which considers the mechanism of plastic deformation and creep deformation has developed. The systematic scheme for numerical analysis of unified model is necessary because the dominant failure mechanism is the defect growth and coalescence in materials. In the present study, the unified viscoplastic model for materials with defects suggested by Suquet and Michel was employed for numerical analysis. The constitutive equations are integrated based on the generalized mid-point rule and implemented into a finite element program (ABAQUS) by means of user-defined subroutine (UMAT). To evaluate the validity of the developed UMAT code and the assessment of the adopted viscoplastic model, the results obtained from the UMAT code was compared with the numerical reference solution and experimental data. The unit cell analysis also has been investigated to study the effect of strain rate, temperature, stress triaxiality and initial defect volume fraction on the growth and coalescence of the defect.

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1001-1015
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• 2009

In this paper, two hybrid difference schemes on the Shishkin mesh are constructed for solving a weakly coupled system of two singularly perturbed convection-diffusion second order ordinary differential equations with a small parameter multiplying the highest derivative. We prove that the schemes are almost second order convergence in the supremum norm independent of the diffusion parameter. Error bounds for the numerical solution and its derivative are established. Numerical results are provided to illustrate the theoretical results.

• Journal of Korean Society on Water Environment
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• v.29 no.4
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• pp.514-522
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• 2013

The major 24 tributaries in Nam-River mid-watershed were monitored for discharge and water quality in order to understand the characteristics of the watershed and to select the tributary catchment for improving water quality. According to the analytical results of discharge and water quality monitoring data of 24 tributaries, the mean value of discharge below $0.1m^3/s$ was 62.5% among the monitored tributaries and it mostly exceeded the water quality standards of Nam-river mid-watershed ($BOD_5$ = 3 mg/L, T-P = 0.1 mg/L over). According to the stream grouping method and the water quality delivery load density ($kg/day/km^2$) based on the results of tributary discharge and water quality monitoring, the tributary watersheds for improving the water quality were selected. In the Nam-River mid-watershed, tributaries in the GaJwaCheon, HaChonCheon catchment (Group D, $BOD_5$ = 3 mg/L over) and in the UirYeongCheon, SeokGyoCheon catchment (Group A, T-P = 0.1 mg/L over), which have a small flow (and/or large flow) and a high concentrations of water pollutants. The various water quality improving scheme for tributaries, in accordance with the reduction of potential point source pollution by living sewage and livestock wastewater, should be established and implemented.

• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.61-69
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• 2000

The free-surface boundary conditions are persistent problem in elastic wave equation modeling by finite-difference method, which can be summarized with the degradation of the accuracy of the solution and limited stability range in Poisson's ratio. In this paper, we propose the mid-point averaging scheme as an alternative way of implementing the free-surface boundary conditions, and present the solution to Lamb's problem to verify our approach.

• Wind and Structures
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• v.9 no.4
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• pp.315-330
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• 2006

Flow and scalar dispersion around Cheomseongdae are numerically investigated using a three-dimensional computational fluid dynamics (CFD) model with the renormalization group (RNG) $k-{\varepsilon}$ turbulence closure scheme. Cheomseongdae is an ancient astronomical observatory in Gyeongju, Korea, and is chosen as a model obstacle because of its unique shape, that is, a cylinder-shaped architectural structure with its radius varying with height. An interesting feature found is a mid-height saddle point behind Cheomseongdae. Different obstacle shapes and corresponding flow convergences help to explain the presence of the saddle point. The predicted size of recirculation zone formed behind Cheomseongdae increases with increasing ambient wind speed and decreases with increasing ambient turbulence intensity. The relative roles of inertial and eddy forces in producing cavity flow zones around an obstacle are conceptually presented. An increase in inertial force promotes flow separation. Consequently, cavity flow zones around the obstacle expand and flow reattachment occurs farther downwind. An increase in eddy force weakens flow separation by mixing momentum there. This results in the contraction of cavity flow zones and flow reattachment occurs less far downwind. An increase in ambient wind speed lowers predicted scalar concentration. An increase in ambient turbulence intensity lowers predicted maximum scalar concentration and acts to distribute scalars evenly.

• Steel and Composite Structures
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• v.9 no.2
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• pp.131-158
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• 2009

This paper presents a modelling technique for the nonlinear analysis of composite steel-concrete beams with partial shear interaction. It extends the applicability of two stiffness elements previously derived by the authors using the direct stiffness method, i.e. the 6DOF and the 8DOF elements, to account for material nonlinearities. The freedoms are the vertical displacement, the rotation and the slip at both ends for the 6DOF stiffness element, as well as the axial displacement at the level of the reference axis for the 8DOF stiffness element. The solution iterative scheme is based on the secant method, with the convergence criteria relying on the ratios of the Euclidean norms of both forces and displacements. The advantage of the approach is that the displacement and force fields of the stiffness elements are extremely rich as they correspond to those required by the analytical solution of the elastic partial interaction problem, thereby producing a robust numerical technique. Experimental results available in the literature are used to validate the finite element proposed in the paper. For this purpose, those reported by Chapman and Balakrishnan (1964), Fabbrocino et al. (1998, 1999) and Ansourian (1981) are utilised; these consist of six simply supported beams with a point load applied at mid-span inducing positive bending moment in the beams, three simply supported beams with a point load applied at mid-span inducing negative bending moment in the beams, and six two-span continuous composite beams respectively. Based on these comparisons, a preferred degree of discretisation suitable for the proposed modelling technique expressed as a function of the ratio between the element length and depth is proposed, as is the number of Gauss stations needed. This allows for accurate prediction of the nonlinear response of composite beams.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.49 no.1
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• pp.21-30
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• 2021

Mid-course trajectory of the missiles equipped with seeker should be designed to detect target within FOV of seeker and to maximize the maneuverability at the point of transition to terminal guidance phase. Because the trajectory optimization problems are generally hard to obtain the analytic solutions due to its own nonlinearity with several constraints, the various numerical methods have been presented so far. In this paper, mid-course trajectory optimization problem for boost-glide missiles is calculated by using SOCP (Second-Order Cone Programming) which is one of convex optimization methods. At first, control variable augmentation scheme with a control constraint is suggested to reduce state variables of missile dynamics. And it is reformulated using a normalized time approach to cope with a free final time problem and boost time problem. Then, partial linearization and lossless convexification are used to convexify dynamic equation and control constraint, respectively. Finally, the results of the proposed method are compared with those of state-of-the-art nonlinear optimization method for verification.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.43 no.2
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• pp.159-168
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• 2010

This paper presents a mathematical model and simulation method for investigating the performance of set net systems and fish cage systems influenced by currents and waves. Both systems consist of netting, mooring ropes, a floating collar and sinkers. The netting and ropes were considered flexible structures and the floating collar was considered an elastic structure. Both were modeled on a mass-spring model. The structures were divided into finite elements and mass points were placed at the mid-point of each element, and the mass points were connected by mass-less springs. Each mass point was subjected to external and internal forces and the total force was calculated at every integration step. An implicit integration scheme was used to solve the nonlinear dynamic system. The computation method was applied to dynamic simulation of actual systems simultaneously influenced by currents and waves in order to evaluate their practicality. The simulation results improved our understanding of the behavior of the structure and provided valuable information concerning the optimized design of set net and fish cage systems exposed to an open ocean environment.