• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.5
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• pp.1551-1562
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• 1991

최근까지 발표된 유한 요소법을 이용한 압연 해석 관련 주요 논문들을 정리해 보면 다음과 같다. Li와 Kobayashil는 강소성 유한 요소법(rigidplastic finite element method)을 여러가지 마찰조건에 대하여 해석하였다. 이때 압연롤은 강체 (rigid body)로 시편은 가공경화(workhardening)를 동반한 강소성체로 모델링하였다. Hwang과 Kobayashi는 강소성 유한 요소법을 이용한 평면 변형 압연에서 재료 손실을 최소화하는 예비 성형체(preform)의 설계에 대한 연구를 수행하였다. 이 경우에도 역시 압연롤은 강체로 시편은 가공 경화를 동반한 강소성체와 완전 소성체로 모델링 되었으나, 고착(sticking) 마찰 조건에 대해서만 해석을 수행하였다. Mori와 Osak- ada 그리고 Oda는 약간 압축성이 있는 재료의 평면 변형 압연에 대하여 연구하였다. 이때 압연롤은 강체로 시편은 가공 경화를 동반한 강소성체로 모델링 되었으며 경계 면에서는 Coulomb 마찰을 고려하였다. 이밖에도 오일러(Eulerian) 수식화를 이용한 Dawson과 Thompson, Berman의 해석 결과가 있으며, 또 폭 방향의 변형까지를 고려한 Li와 Kobayashi, Mori와 Osakada의 3차원 해석 결과가 있다.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.7 s.94
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• pp.1700-1709
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• 1993

The stepped specimen which is subjected to step loading is modeled to study the initiation and growth of adiabatic shear band using explicit time integration finite element method. Three different clearance sizes are tested. The material model for the stepped specimen includes effects of strain hardening, strain rate hardening and thermal softening. It is found that the material inside the fully grown adiabatic shear band experiences three phase of deformation, (1) homogeneous deformation phase, (2) initiation/incubation phase, and (3) fast growth phase. The second phase of deformation is initiated after sudden shear stress drop which occurs at the same time regardless of the clearance size. The incubation time prior to fast growth phase increases, as the clearance size of the stepped specimen increases. Whereas, after incubation period, the growth rate of the adiabatic shear band decreases, as the clearance size decreases. It is also found that two adiabatic shear band may develop instead of one for the smaller clearance size.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2002.02a
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• pp.274-284
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• 2002

Deep drawing process for rectangular drawn section is different with that for axisymmetric circular one. Therefore deep drawing process for rectangular drawn section requires several intermediate steps to generate the final configuration without any significant defect. In this study, finite element analysis for multi-stage deep drawing process for high precision rectangular cases is carried out especially for an extreme aspect ratio. The analysis is performed using rigid-plastic finite element method with an explicit time integration scheme of the commercial program, LS-DYNA3D. The sheet blank is modeled using eight-node continuum brick elements. The results of analysis show that the irregular contact condition between blank and die affects the occurrence of failure, and the difference of aspect ratio in the drawn section leads to non-uniform metal flow, which may cause failure. A series of experiments for multi-stage deep drawing process for the rectangular cases are conducted, and the deformation configuration and the thickness distribution of the drawn rectangular cases are investigated by comparing with the results of the numerical analysis. The numerical analysis with an explicit time integration scheme shows good agreement with the experimental observation.

• Structural Engineering and Mechanics
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• v.37 no.2
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• pp.197-213
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• 2011

Concrete is a heterogeneous material exhibiting quasi-brittle behaviour. While homogenization of concrete is commonly accepted in general engineering applications, a detailed description of the material heterogeneity using a mesoscale model becomes desirable and even necessary for problems where drastic spatial and time variation of the stress and strain is involved, for example in the analysis of local damages under impact, shock or blast load. A mesoscale model can also assist in an investigation into the underlying mechanisms affecting the bulk material behaviour under various stress conditions. Extending from existing mesoscale model studies, where use is often made of specialized codes with limited capability in the material description and numerical solutions, this paper presents a mesoscale computational model developed under a general-purpose finite element environment. The aim is to facilitate the utilization of sophisticated material descriptions (e.g., pressure and rate dependency) and advanced numerical solvers to suit a broad range of applications, including high impulsive dynamic analysis. The whole procedure encompasses a module for the generation of concrete mesoscale structure; a process for the generation of the FE mesh, considering two alternative schemes for the interface transition zone (ITZ); and the nonlinear analysis of the mesoscale FE model with an explicit time integration approach. The development of the model and various associated computational considerations are discussed in this paper (Part 1). Further numerical studies using the mesoscale model for both quasi-static and dynamic loadings will be presented in the companion paper (Part 2).

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.211-229
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• 2011

In this paper, we present a new explicit procedure using periodic cubic B-spline interpolation polynomials to solve linear and nonlinear dynamic equation of motion governing single degree of freedom (SDOF) systems. In the proposed approach, a straightforward formulation was derived from the approximation of displacement with B-spline basis in a fluent manner. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. Actually, this method lies in the case of conditionally stable methods. A simple step-by-step algorithm is implemented and presented to calculate dynamic response of SDOF systems. The validity and effectiveness of the proposed method is demonstrated with four examples. The results were compared with those from the numerical methods such as Duhamel integration, Linear Acceleration and also Exact method. The comparison shows that the proposed method is a fast and simple procedure with trivial computational effort and acceptable accuracy exactly like the Linear Acceleration method. But its power point is that its time consumption is notably less than the Linear Acceleration method especially in the nonlinear analysis.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.23 no.2
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• pp.93-114
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• 2019

In this article, we introduce a finite difference method for solving the Navier-Stokes equations in rectangular domains. The method is proved to be energy stable and shown to be second-order accurate in several benchmark problems. Due to the guaranteed stability and the second order accuracy, the method can be a reliable tool in real-time simulations and physics-based animations with very dynamic fluid motion. We first discuss a simple convection equation, on which many standard explicit methods fail to be energy stable. Our method is an implicit Runge-Kutta method that preserves the energy for inviscid fluid and does not increase the energy for viscous fluid. Integration-by-parts in space is essential to achieve the energy stability, and we could achieve the integration-by-parts in discrete level by using the Marker-And-Cell configuration and central finite differences. The method, which is implicit and second-order accurate, extends our previous method [1] that was explicit and first-order accurate. It satisfies the energy stability and assumes rectangular domains. We acknowledge that the assumption on domains is restrictive, but the method is one of the few methods that are fully stable and second-order accurate.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.8
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• pp.1519-1529
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• 1992

A stepped specimen which is subjected to step loading is modeled to study the initiation and growth of adiabatic shear band using explicit time integration finite element code. The material model for specimen includes effects of thermal softening, strain hardening and strain rate hardening. Various mesh sizes are tested to check whether they are small enough to model highly localized discontinuous phenomena reasonably well. It is shown that the number of adiabatic shear band depends on impact velocity and it is also shown that the initiation and growth of adiabatic shear band inversely depends on prescribed velocity at the top of specimen.

• Earthquakes and Structures
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• v.7 no.2
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• pp.159-178
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• 2014

Although the family methods with unconditional stability and numerical dissipation have been developed for structural dynamics they all are implicit methods and thus an iterative procedure is generally involved for each time step. In this work, a new family method is proposed. It involves no nonlinear iterations in addition to unconditional stability and favorable numerical dissipation, which can be continuously controlled. In particular, it can have a zero damping ratio. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it can save many computationally efforts when compared to the currently available dissipative implicit integration methods.

• Earthquakes and Structures
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• v.14 no.1
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• pp.45-53
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• 2018

A family of the structure-dependent methods seems very promising for time integration since it can simultaneously have desired numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and numerical dissipation. However, an unusual overshoot, which is essentially different from that found by Goudreau and Taylor in the transient response, has been experienced in the steady-state response of a high frequency mode. The root cause of this unusual overshoot is analytically explored and then a remedy is successfully developed to eliminate it. As a result, an improved formulation of this family method can be achieved.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.1
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• pp.93-102
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• 2020

The concept of temperature distribution in inhomogeneous semi-infinite solids is examined by making use of direct integration method. The analysis is done on the solution of the in-plane steady state heat conduction problem under certain boundary conditions. The method of direct integration has been employed, which is then reduced to Volterra integral equation of second kind, produces the explicit form analytical solution. Using resolvent- kernel algorithm, the governing equation is solved to get present solution. The temperature distribution obtained and calculated numerically and the relation with distribution of heat flux generated by internal heat source is shown graphically.