• 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 Materials Processing
• /
• v.9 no.3
• /
• pp.274-283
• /
• 2000

A dynamic explicit finite element code for simulating sheet forming processes has been developed. The code utilizes 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 is built for each tool at the initial stage of the analysis. hierarchical structure is built in a way to divide a box to 8 sub-boxes, 2 in each direction, until the lowest level of the hierarchical structure contains exactly one segment of the tool or empty. Then at each time step, contact is checked from the box to sub-boxes hierarchically for each node. Comparisons of computational results of various examples with the existing ones show the validity of the method.

• 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.

• 한국신재생에너지학회:학술대회논문집
• /
• 2008.05a
• /
• pp.315-318
• /
• 2008

Numerical calculation for the 1MW class horizontal axis wind turbine blade has been carried out to estimate the magnitude between discrete noise and random noise. Farassat formula 1A was adopted to get the discrete noise signal, and blade element momentum theory was used to obtain the distribution of the aerodynamic data along the blade span. Fukano's approach was also adopted to calculate the unsteady aerodynamic random noise due to the Karman vortex generation at the trailing edge of the wind turbine blade. From the noise prediction for the 1MW class horizontal axis wind turbine, the frequency band of the discrete noise lies in the infrasound region, and that of the random noise lies in the audible band region.

• Structural Engineering and Mechanics
• /
• v.3 no.4
• /
• pp.359-372
• /
• 1995

This study presents an efficient method for optimum design of plate and shell structures, when the design variables are continuous or discrete. Both sizing and shape design variables are considered. First the structural responses such as element forces are approximated in terms of some intermediate variables. By substituting these approximate relations into the original design problem, an explicit nonlinear approximate design task with high quality approximation is achieved. This problem with continuous variables, can be solved by means of numerical optimization techniques very efficiently, the results of which are then used for discrete variable optimization. Now, the approximate problem is converted into a sequence of second level approximation problems of separable form and each of which is solved by a dual strategy with discrete design variables. The approach is efficient in terms of the number of required structural analyses, as well as the overall computational cost of optimization. Examples are offered and compared with other methods to demonstrate the features of the proposed method.

• Kyungpook Mathematical Journal
• /
• v.47 no.4
• /
• pp.529-548
• /
• 2007

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

• Journal of the Korean Mathematical Society
• /
• v.59 no.3
• /
• pp.519-548
• /
• 2022

In this paper, a stabilized-penalized collocated finite volume (SPCFV) scheme is developed and studied for the stationary generalized Navier-Stokes equations with mixed Dirichlet-traction boundary conditions modelling an incompressible biological fluid flow. This method is based on the lowest order approximation (piecewise constants) for both velocity and pressure unknowns. The stabilization-penalization is performed by adding discrete pressure terms to the approximate formulation. These simultaneously involve discrete jump pressures through the interior volume-boundaries and discrete pressures of volumes on the domain boundary. Stability, existence and uniqueness of discrete solutions are established. Moreover, a convergence analysis of the nonlinear solver is also provided. Numerical results from model tests are performed to demonstrate the stability, optimal convergence in the usual L² and discrete H¹ norms as well as robustness of the proposed scheme with respect to the choice of the given traction vector.

• International Journal of Aeronautical and Space Sciences
• /
• v.7 no.1
• /
• pp.106-117
• /
• 2006

The active vibration control of composite shell structure has been performed with the optimized sensor/actuator system. For the design of sensor/actuator system, a method based on finite element technique is developed. The nine-node Mindlin shell element has been used for modeling the integrated system of laminated composite shell with PVDF sensor/actuator. The distributed selective modal sensor/actuator system is established to prevent the effect of spillover. Electrode patterns and lamination angles of sensor/actuator are optimized using genetic algorithm. Continuous electrode patterns are discretized according to finite element mesh, and orientation angle is encoded into discrete values using binary string. Sensor is designed to minimize the observation spillover, and actuator is designed to minimize the system energy of the control modes under a given initial condition. Modal sensor/actuator for the first and the second mode vibration control of singly curved cantilevered composite shell structure are designed with the method developed on the finite element method and optimization. For verification, the experimental test of the active vibration control is performed for the composite shell structure. Discrete LQG method is used as a control law.

• 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.

• Journal of Ocean Engineering and Technology
• /
• v.34 no.6
• /
• pp.481-488
• /
• 2020

Composite materialsuch as glass-fiber reinforced plastic and carbon-fiber reinforced plastic (CFRP) shows anisotropic property and have been widely used for structural members and outfitings of ships. The structural safety of composite structures has been generally evaluated via finite element analysis. This paper presents a technique for updating the finite element model of anisotropic beams or plates via natural frequencies. The finite element model updates involved a compensation process of anisotropic material properties, such as the elastic and shear moduli of orthotropic structural members. The technique adopted was based on a discrete genetic algorithm, which is an optimization technique. The cost function was adopted to assess the optimization problem, which consisted of the calculated and referenced low-order natural frequencies for the target structure. The optimization process was implemented with MATLAB, which includes the finite element updates and the corresponding natural frequency calculations with MSC/NASTRAN. Material properties of a virtual cantilevered orthotropic beam were estimated to verify the presented method and the results obtained were compared with the reference values. Furthermore, the technique was applied to a cantilevered CFRP beam to successfully estimate the unknown material properties.