• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1057-1062
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• 2008

Representing a complex, three-dimensional shape, such as an automobile, requires a large amount of CAD data consisting of millions of approximated discontinuous points, which makes it difficult or even impossible to efficiently optimize the entire shape. For this reason, in this paper, function based design method is proposed to optimize the external shape of an automobile. A vehicle modeling function was defined in the form of a Bernstein polynomial to smoothly express the complex 2D and 3D automobile configurations. The sub-sectional parts of the vehicle modeling function are defined as section functions through classifying each subsection of a box model. It is shown that the use of the vehicle modeling functions has the useful advantages in an aerodynamic shape optimization.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1361-1366
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• 2008

Failure mechanism of the poor contact is analyzed on the basis of used connectors and this poor contact of connectors is reappeared by the new forced fretting wear method. As the result of failure analysis and reappearance, fretting wear and corrosion of the contact interface causes the contact resistance degradation and the poor contact of connectors. The amount of degradation depends on the fretting stroke. Changes in contact resistance of static contacts are likely to be small and gradual, while motions of contact interface may result in larger and discontinuous changes in resistance and voltage. This voltage drop by fretting motions is large enough to cause the distortion of sensor signal and mis-working of electric components.

• Smart Structures and Systems
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• v.19 no.5
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• pp.577-585
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• 2017

In this paper, an adaptive fuzzy sliding mode controller (AFSMC) is designed to reduce dynamic responses of seismically excited structures. In the conventional sliding mode control (SMC), direct implementation of switching-type control law leads to chattering phenomenon which may excite unmodeled high frequency dynamics and may cause vibration in control force. Attenuation of chattering and its harmful effects are done by using fuzzy controller to approximate discontinuous part of the sliding mode control law. In order to prevent time-consuming obtaining of membership functions and reduce complexity of the fuzzy rule bases, adaptive law based on Lyapunov function is designed. To demonstrate the performance of AFSMC method and to compare with that of SMC and fuzzy control, a linear three-story scaled building is investigated for numerical simulation based on the proposed method. The results indicate satisfactory performance of the proposed method superior to those of SMC and fuzzy control.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.

• Bulletin of the Korean Mathematical Society
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• v.37 no.2
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• pp.229-247
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• 2000

This paper is concerned with the impulsive Cauchy problem where the control function u is a possibly discontinuous vector-valued function with finite total variation. We assume that the vector fields f, $g_i$(i=1,…, m) are dependent on the time variable. The impulsive Cauchy problem is of the form x(t)=f(t,x) +$\SUMg_i(t,x)u_i(t)$, $t\in$[0,T], x(0)=$\in\; R^n$, where the vector fields f, $g_i$ : $\mathbb{R}\; \times\; \mathbb{R}\; \longrightarrow\; \mathbb(R)^n$ are measurable in t and Lipschitz continuous in x, If $g_i's$ satisfy a condition that $\SUM{\mid}g_i(t_2,x){\mid}{\leq}{\phi}$ $\forallt_1\; <\; t-2,x\; {\epsilon}\;\mathbb{R}^n$ for some increasing function $\phi$, then the imput-output function can be continuously extended to measurable functions of bounded variation.

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.467-475
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• 2008

The aim of the present paper is three fold. Firstly, we obtain common fixed point theorems for a pair of selfmaps satisfying nonexpansive or Lipschitz type condition by using the notion of pointwise R-weak commutativity but without assuming the completeness of the space or continuity of the mappings involved (Theorem 1, Theorem 2 and Theorem 3). Secondly, we generalize the results obtained in first three theorems for four mappings by replacing the condition of noncompatibility of maps with the property (E.A) and using the R-weak commutativity of type $(A_g)$ (Theorem 4). Thirdly, in Theorem 5, we show that if the aspect of noncompatibility is taken in place of the property (E.A), the maps become discontinuous at their common fixed point. We, thus, provide one more answer to the problem posed by Rhoades [11] regarding the existence of contractive definition which is strong enough to generate fixed point but does not forces the maps to become continuous.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.773-778
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• 2009

Recently, Xue et al. [Computers and Mathematics with Applications 55 (2008) 1215-1224] proposed a formula for the expected value of a function of a fuzzy variable based on the assumption that the fuzzy variable has a continuous membership function. In conclusion, they remained the case where the membership function of the fuzzy variable is discontinuous for the future research, and then expected to get similar results. Thus this note is to propose a new formula for the expected value of a function of a general fuzzy variable which is not restricted on having a continuous membership function. Furthermore, we give an example which cannot be applied to the formula that Xue et al. proposed. We also use the same example given by Xue et al. to show how to apply the new formula.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2005.06a
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• pp.287-292
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• 2005

In this paper, a state steering strategy using digital control method for chained system is presented. The chained system can be derived from the velocity or acceleration constraints that cannot be integrable. Especially, the chained system derived from an acceleration constraints is called the high order chained system. Such a system classified as a nonholonomic systems and cannot be controlled to its equilibrium points by continuous and time-invariant controller. Therefore discontinuous and time varying controller should be applied to control nonholonomic system. Using variable transformation, two sub system can be obtained from the chained or high order chained system. Deadbeat control and iterative state steering methods are proposed to control the systems that obtained from the variable transformation. Simulation results are given to show the effectiveness of the proposed control scheme.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.458-463
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• 2000

The mechanical structures generally have discontinuous parts such as the cracks, notches and holes owing to various reasons. In this paper, in order to analyze effectively these singularity problems using the finite element method, a mixed analysis method which an analytical solution and finite element solutions are simultaneously used is newly proposed. As the analytical solution is used in the singularity region and the finite element solutions are used in the remaining regions except this singular zone, this analysis method reasonably provides for the numerical solution of a singularity problem. Through various numerical examples, it is shown that the proposed analysis method is very convenient and gives comparatively accurate solution.

• Korean Journal of Materials Research
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• v.8 no.3
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• pp.238-244
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• 1998

Sn-rich합금의 석출 현상을 조사하였다. 첫째, 대기중과 진공 중에서 용해된 90Sn-o10Bi(wt%)합금을 $140^{\circ}C$에서 용체화 처리한 후 석출반응을 조사하였다. 90Sn-10Bi(wt%)합금은 불연속 석출(DP)현상을 나타냈다. 공기 중에서 용융된 시료의 DP반응이 진공 중에서 용융된 시료보다 빠르게 진행되었다. 이것은 공기 중에서 용융하는 과정에서 시료에 용존된 산소에 의해 입계 에너지가 감소한 것에 기인하는 것으로 판단된다. 둘째, 용융 후 서냉 응고된 Sn-Bi(-In)합금을 $140^{\circ}C$이하의 온도에서 열처리하여 미세조직 변화를 조사하였다. 명확한 고경각 입계가 존재하지 않는 응고조직에서, 편석영역으로부터 DP반응이 진행되어 석출셈이 형성되었다. DP반응선단에는 반응계면이 관찰되었다. 이 현상은, 이제까지 알려진 바와는 다르게, DP반응이 반응 전에 존재하는 고경각 입계뿐만 아니라 재결정현상에 의해 새로운 석출계면이 생성될 수 있음을 의미한다. 이러한 재결정 현상은 확산에 의한 정합변형(coherency strain)으로 설명된다.