• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.850-858
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• 1997

A new a posteriori error estimator is introduced and applied to variational inequalities occurring in problems of flow through porous media. In order to construct element-wise a posteriori error estimates the global error is localized by a special mixed formulation in which continuity conditions at interfaces are treated as constraints. This approach leads to error indicators which provide rigorous upper bounds of the element errors. A discussion of a compatibility condition for the well-posedness of the local error analysis problem is given. Two numerical examples are solved to check the compatibility of the local problems and convergence of the effectivity index both in a local and a global sense with respect to local refinements.

• Korean Journal of Computational Design and Engineering
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• v.5 no.4
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• pp.393-402
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• 2000

Recently 5-axis NC machines are widely used in Korea. Since 5-axis machines have two more degrees of freedom than 3-axis machines, it is very important to find desirable tool positions(locations and orientations) in order to make an efficient use of expensive 5-axis NC machines. In this research an algorithm to determine “optimal” tool positions for 5-axis machining of sculptured surfaces is developed. For given CC(Cutter Contact) points, this algorithm determines the cutter axis vectors which minimize cusp heights and satisfy constraints. To solve the optimal problem, we deal with following major issues: (1) an approximation method of a cusp height as a measure of optimality (2) Identifying some properties of the optimal problem (3) a search method for the optimal points using the properties. By using a polyhedral model as a machining surface, this algorithm applies to sculptured surfaces covering: overhanged surface.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1994.10a
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• pp.852-859
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• 1994

Optmal topology design is to search the optimal layout of the structure which can be used fot the shape of the conceptual design stage. Our objective is to maximize the stiffness of the structure under a material usage constraint. The density of each finite element is the design variable and its relationship with Young's modulus is expressed by quadratic form. The shape is represented by the entire density distribution, the structural analysis is performed by finite element method and the optimization is achieved by feasible direction method. Unlike optimality criteria method,feasible direction method can handle various problems simultaneously, that is, multi- objectives and multi-constraints. Total optimization time can be reduced by the approximation of the material property and fewer design variables than homogenization method. Topology optimization is applied to design the shape of ribs.

• Korean Journal of Computational Design and Engineering
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• v.19 no.3
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• pp.245-252
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• 2014

Engineering applications of global optimization techniques are recently abundant in the literature and it may be caused by both new methodologies arising and faster computers coming out. Many of the optimization techniques are based on natural or biological phenomena. This study put focus on enhancing the performace of Cuckoo Search (CS) among them since it has the least number of parameters to tune. The proposed enhancement can be achieved by applying surrogate-based optimization at every cycle of CS, which fortifies the exploitation capability of the original method. The enhanced algorithm has been applied several engineering design problems with constraints. The proposed method shows comparable or superior performance to the original method.

• Journal of Ocean Engineering and Technology
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• v.27 no.1
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• pp.85-92
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• 2013

This paper deals with the resonant type of a WEC (wave energy converter) and the determination method of its geometric parameters which were obtained to construct the robust and optimal structure, respectively. In detail, the optimization problem is formulated with the constraints composed of the response surfaces which stand for the resonance period(heave, pitch) and the meta center height of the buoy. Use of a signal-to-noise ratio calculated from normalized multi-objective results with the weight factor can help to select the robust design level. In order to get the sample data set, the motion responses of the power buoy were analyzed using the BEM (boundary element method)-based commercial code. Also, the optimization result is compared with a robust design for a feasibility study. Finally, the power efficiency of the WEC with the optimum design variables is estimated as the captured wave ratio resulting from absorbed power which mainly related to PTO (power take off) damping. It could be said that the resultant of the WEC design is the economical optimal design which satisfy the given constraints.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.43 no.4
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• pp.23-32
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• 2020

Many small and medium-sized manufacturing companies process various product types to respond different customer orders in a single production line. To improve their productivity, they often apply batch processing while considering various product types, constraints on batch sizes and setups, and due date of each order. This study introduces a batch scheduling heuristic for a production line with multiple product types and different due dates of each order. As the process times vary due to the different batch sizes and product types, a recursive equation is developed based on a flow line model to obtain the upper bound on the completion times with less computational complexity than full computation. The batch scheduling algorithm combines and schedules the orders with same product types into a batch to improve productivity, but within the constraints to match the due dates of the orders. The algorithm incorporates simple and intuitive principles for the purpose of being applied to small and medium companies. To test the algorithm, two case studies are introduced; a high pressure coolant (HPC) manufacturing line and a press process at a plate-type heat exchanger manufacturer. From the case studies, the developed algorithm provides significant improvements in setup frequency and thus convenience of workers and productivity, without violating due dates of each order.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.6
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• pp.2595-2618
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• 2018

In this paper, we investigate secure communication with the presence of multiple eavesdroppers (Eves) in a two-tier downlink dense heterogeneous network, wherein there is a macrocell base station (MBS) and multiple femtocell base stations (FBSs). Each base station (BS) has multiple users. And Eves attempt to wiretap a macrocell user (MU). To keep Eves ignorant of the confidential message, we propose a physical-layer security scheme based on cross-layer cooperation to exploit interference in the considered network. Under the constraints on the quality of service (QoS) of other legitimate users and transmit power, the secrecy rate of system can be maximized through jointly optimizing the beamforming vectors of MBS and cooperative FBSs. We explore the problem of maximizing secrecy rate in both non-colluding and colluding Eves scenarios, respectively. Firstly, in non-colluding Eves scenario, we approximate the original non-convex problem into a few semi-definite programs (SDPs) by employing the semi-definite relaxation (SDR) technique and conservative convex approximation under perfect channel state information (CSI) case. Furthermore, we extend the frame to imperfect CSI case and use the Lagrangian dual theory to cope with uncertain constraints on CSI. Secondly, in colluding Eves scenario, we transform the original problem into a two-tier optimization problem equivalently. Among them, the outer layer problem is a single variable optimization problem and can be solved by one-dimensional linear search. While the inner-layer optimization problem is transformed into a convex SDP problem with SDR technique and Charnes-Cooper transformation. In the perfect CSI case of both non-colluding and colluding Eves scenarios, we prove that the relaxation of SDR is tight and analyze the complexity of proposed algorithms. Finally, simulation results validate the effectiveness and robustness of proposed scheme.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.1
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• pp.31-37
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• 2013

This study aims to find the optimal skirt dimensions for a composite pressure vessel with a separated dome part. The size optimization for the skirt structure of the composite pressure vessel was conducted using a sub-problem approximation method and batch processing codes programmed using ANSYS Parametric Design Language (APDL). The thickness and length of the skirt part were selected as design variables for the optimum analysis. The objective function and constraints were chosen as the weight and the displacement of the skirt part, respectively. The numerical results showed that the weight of the skirt of a composite pressure vessel with a separated dome part could be reduced by a maximum of 4.38% through size optimization analysis of the skirt structure.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.8
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• pp.2113-2122
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• 1994

The 3-D FEM analysis for simulating the stamping operation of planar anisotropic sheet metals with arbitrarily-shaped tools is introduced. An implicit, incremental, updated Lagrangian formulation with a rigid-viscoplastic constitutive equation is employed. Contact and friction are considered through the mesh-normal, which compatibly describes arbitrary tool surfaces and FEM meshes without depending on the explicit spatial derivatives of tool surfaces. The consistent full set of governing relations, comprising equilibrium equation and mesh-normal geometric constraints, is appropriately linearized. The linear triangular elements are used for depicting the formed sheet, based on membrane approximation. Barlat's non-quadratic anisotropic yield criterion(strain-rate potential) is employed, whose in-plane anisotropic properties are taken into account with anisotropic coefficients and non-quadratic function parameter. The planar anisotropic finite element formulation is tested with the numerical simulations of the stamping of an automotive hood inner panel and the drawing of a hemispherical punch. The in-plane anisotropic effects on the formability of both mild steel and aluminum alloy sheet metals are examined.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.