• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.563-578
• /
• 2005

In [Z. Cai and B. C. Shin, SIAM J. Numer. Anal. 40 (2002), 307-318], we developed the discrete first-order system least squares method for the second-order elliptic boundary value problem by directly approximating $H(div){\cap}H(curl)-type$ space based on the Helmholtz decomposition. Under general assumptions, error estimates were established in the $L^2\;and\;H^1$ norms for the vector and scalar variables, respectively. Such error estimates are optimal with respect to the required regularity of the solution. In this paper, we study solution methods for solving the system of linear equations arising from the discretization of variational formulation which possesses discrete biharmonic term and focus on numerical results including the performances of multigrid preconditioners and the finite element accuracy.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.11 no.1
• /
• pp.59-69
• /
• 2019

This paper focuses on the numerical simulation of ice abrasion induced by unbreakable ice floe. Under the assumption that unbreakable floes behave as rigid body, the Discrete Element Method (DEM) was applied to simulate the interaction between a fixed structure and ice floes. DEM is a numerical technique which is eligible for computing the motion and effect of a large number of particles. In DEM simulation, individual ice floe was treated as single rigid element which interacts with each other following the given interaction rules. Interactions between the ice floes and structure were defined by soft contact and viscous Coulomb friction laws. To derive the details of the interactions in terms of interaction parameters, the Finite Element Method (FEM) was employed. An abrasion process between a structure and an ice floe was simulated by FEM, and the parameters in DEM such as contact stiffness, contact damping coefficient, etc. were calibrated based on the FEM result. Resultantly, contact length and contact path length, which are the most important factors in ice abrasion prediction, were calculated from both DEM and FEM and compared with each other. The results showed good correspondence between the two results, providing superior numerical efficiency of DEM.

• Structural Engineering and Mechanics
• /
• v.36 no.3
• /
• pp.343-361
• /
• 2010

The Discrete Element Method adopting particles for the domain discretization has recently been adopted in fracture studies of non-homogeneous continuous media such as concrete and rock. A model is proposed in which the reinforcement is modelled by 1D rigid-spring discrete elements. The rigid bars interact with the rigid circular particles that simulate the concrete through contact interfaces. The DEM enhanced model with reinforcement capabilities is evaluated using three point bending and four point bending tests on reinforced concrete beams without stirrups. Under three point bending, the model is shown to reproduce the expected final crack pattern, the crack propagation and the load displacement diagram. Under four point bending, the model is shown to match the experimental ultimate load, the size effect and the crack propagation and localization.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2007.04a
• /
• pp.789-794
• /
• 2007

Recently, the necessity of efficient and exact method to analyze structures is increasing with the importance of the seismic analysis. But the finite element method used in many field do not give the exact solution unless the length of the element is very short enough to represent the deformation of the element. Because the amount of computer calculation increase with the increasing of the number of degree of freedoms, the finite element method for the exact dynamic analysis of structures would not be efficient. To solve these problems, spectral clement method combined spectral method using the principle of wave mechanics and finite element method for the analysis of discrete models is applied to evaluate the behavior of the spatial structures. As a result of analysis. it becomes clear that the spectral element method is faster and more exact than the finite clement method.

• Journal of the Korean School Mathematics Society
• /
• v.6 no.2
• /
• pp.87-99
• /
• 2003

As the development of computer science discrete mathematics has been developed accordingly. Discrete mathematics is one of the vital element for the development of the computer and IT technologies since it is the theoretical basis for these field of technologies. Currently, according the Seventh Curriculum Standards in Mathematics, high school students may participate in the class of discrete mathematics as one of their optional curriculum. However, discrete mathematics is a new to the most students in high school. Therefore, the teaching methods for the class of discrete mathematics must be carefully designed so that students acknowledge the importance of this new subject. For this purpose, we first show that why the algorithm is needed and then analyze the problem involved in the method of the traditional matrix multiplications. Finally, we suggest two matrix multiplication algorithms which are more efficient than the traditional method.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.21 no.6
• /
• pp.758-772
• /
• 1997

The snapshot method is introduced to approximate the coherent structures of planar forcing jet flow. The numerical simulation of flow field is simulated by discrete vortex method. With snapshot method we could treat the data efficiently and approximate coherent structures inhered in the planer jet flow. By forcing the jet at a sufficient amplitude and at a well-chosen frequency, the paring can be controlled in the region of the jet. Finally we expressed the underlying coherent structures of planar jet flow in the minimum number of modes by Karhunen-Loeve transformation in order to understand jet flow and to make the information storage and management in computers easier.

• Journal of the Korean Geotechnical Society
• /
• v.22 no.6
• /
• pp.63-69
• /
• 2006

In this paper, a method is presented for estimating the bearing capacity of shallow foundations based on the Discrete Element Method (DEM). By applying Winkler-springs for accounting for the compatibility between soil blocks, the proposed method can estimate the state of stress at failure surface and the ultimate bearing capacity. For the investigation of the application of the method, example problems about shallow foundations on the single layer and two layers soil are analyzed.

• 한국신재생에너지학회:학술대회논문집
• /
• 2010.11a
• /
• pp.123.1-123.1
• /
• 2010

수평형 지중열교환기의 최적설계를 위해서는 되메움재의 광물특성 및 입자크기, 열전도도(thermal conductivity), 열용량(heat capacity)등과 같은 열적 특성을 파악 하는 것은 중요하다. 수평형 지중 열교환기용 되메움재의 열전도도를 파악하기 위해 비정상 열선법을 적용한 QTM-500을 사용하여 포화도에 따른 천연규사-물-공기 혼합물의 열전도도를 측정하였다. 측정된 열전도도를 개별요소법(Discrete Element Mothod)에 근거한 2차원 수치해석 프로그램인 PFC2D(Particle Flow Code in 2 Dimension)를 이용하여 비교 분석하였다. 수치해석에서는 혼합물의 건조밀도를 일정하게 유지한 상태에서 포화도에 따라 가상의 물 입자 개수를 변화시켰다. 개별요소법을 이용한 열전달 수치해석에서는 입자의 접촉을 통해 발생한 thermal pipe에 의해 열전달이 이루어진다. 이러한 thermal pipe의 열전도도는 접촉된 두 입자의 열전도도와 접촉면의 평균 열전도도를 고려하여 적용하였다.

• Journal of KSNVE
• /
• v.7 no.4
• /
• pp.637-644
• /
• 1997

In this paper, a method of finite element analysis is presented for efficient calculation of vibration characteristics of not only simply interconnected structure with cyclic symmetry but also multiply interconnected structure with cyclic symmetry by using discrete Fourier trandform by means of a computer with small memory in a short time. Simply interconnected structure means it is composed of substructures which are adjacent themselves in circumferential direction. First, a mathematical model of multiply interconnected structure with cyclic symmetry is defined. The multiply interconnected structure is partitioned into substructures with the same goemetric configuration and constraint eqauations to be satisfied on connecting boundaries are defined. Nodal displacements and forces are transformed into complex forms through discrete Fourier transform and then finite element analysis is performed for just only a representative substructure. In free vibration analysis, natural frequencies of a whole structure can be obtained through a series of calculation for a substructure along the number of nodal diameter. And in forced vibration analysis, forced response of whole structure can be achieved by using inverse discrete Fourier transform of results which come from analysis for a substructure.

• Proceedings of the Korean Society for Technology of Plasticity Conference
• /
• 1999.03b
• /
• pp.22-25
• /
• 1999

A dynamic explicit finite element code for simulating sheet forming processes has been developed The code utilises the discrete Kirchhoff shell element and contact force is treated by a conventional penalty method. In order to reduce the computational cost a new and robust contact searching algorithm has been developed and implemented into the code. in the method a hierarchical structure of tool segments called a tree structure is built for each tool at the initial stage of the analysis Tree is built in a way to divide a trunk to 8 sub-trunk 2 in each direction until the lowest level of the tree(leaf) contains exactly one segment of the tool. In order to have a well-balanced tree each box on each sub level contains one eighth of the segments. Then at each time step contact line from a node comes out of the surface of the tool. Simulation of various sheet forming processes were performed to verify the validity of the developed code with main focus on he usefulness of the developed contact searching algorithm.