• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.3
• /
• pp.327-364
• /
• 2015

In this paper, a generalized guidance law with an arbitrary pair of guidance coefficients for impact angle control is proposed. Under the assumptions of a stationary target and a lag-free missile with constant speed, necessary conditions for the guidance coefficients to satisfy the required terminal constraints are obtained by deriving an explicit closed-form solution. Moreover, optimality of the generalized impact-angle control guidance law is discussed. By solving an inverse optimal control problem for the guidance law, it is found that the generalized guidance law can minimize a certain quadratic performance index. Finally, analytic solutions of the generalized guidance law for a first-order lag system are investigated. By solving a third-order linear time-varying ordinary differential equation, the blowing-up phenomenon of the guidance loop as the missile approaches the target is mathematically proved. Moreover, it is found that terminal misses due to the system lag are expressed in terms of the guidance coefficients, homing geometry, and the ratio of time-to-go to system time constant.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• pp.345-360
• /
• 2018

In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

• Structural Engineering and Mechanics
• /
• v.73 no.1
• /
• pp.83-95
• /
• 2020

In this work, a mathematical model of beam-column system carrying a double eccentric end mass system is investigated, and solved analytically based on the exact solution analysis. The model considers the case in which the double eccentric end mass is a rigid storage tank containing fluid. Both Timoshenko and Bernoulli-Euler beam bending theories are considered. Equation of motion, general solution and boundary conditions for the present system model are developed and presented in dimensional and non-dimensional format. Several important non-dimensional design parameters are introduced. Symbolic and/or explicit formulae of the frequency and mode shape equations are formulated. To the authors knowledge, the present reduced closed form symbolic and explicit frequency equations have not appeared in literature. For different applications, the results are validated using commercial finite element package, namely ANSYS. The beam-column system investigated in this paper is significant for many engineering applications, especially, in mechanical and structural systems.

• Proceedings of the Korean Society of Computer Information Conference
• /
• 2019.01a
• /
• pp.333-335
• /
• 2019

본 논문에서는 많은 개체와의 충돌검사를 요구하는 입자 기반 시스템에서 부채꼴 영역의 동적인 변화를 이용하여 효율적으로 충돌검사를 가속화시킬 수 있는 프레임워크를 제안한다. 부채꼴 영역의 동적인 변화를 계산하기 위해 입자의 위치와 속도를 이용하여 부채꼴의 영역을 결정하였으며, 이 영역 내에 있는 입자들만을 이용하여 충돌 검사를 빠르게 수행한다. 본 연구에서 제안하는 가속화 방법은 트리 자료구조를 명시적으로 만들지 않고, 닫힌 형태 방정식(Closed form equation)으로 실행되기 때문에 간단하게 구현되며 모든 결과에서 충돌검사 성능이 3배 정도 개선되었다.

• Structural Engineering and Mechanics
• /
• v.69 no.2
• /
• pp.121-129
• /
• 2019

The present study investigates the propagation of shear waves in a composite structure comprised of imperfectly bonded piezoelectric layer with a micropolar half space. Piezoelectric layer is considered to be initially stressed. Micropolar theory of elasticity has been employed which is most suitable to explain the size effects on small length scale. The general dispersion equations for the existence of waves in the coupled structure are obtained analytically in the closed form. Some particular cases have been discussed and in one particular case the dispersion relation is in well agreement to the classical-Love wave equation. The effects of various parameters viz. initial stress, interfacial imperfection and micropolarity on the phase velocity are obtained for electrically open and mechanically free system. Numerical computations are carried out and results are depicted graphically to illustrate the utility of the problem. The phase velocity of the shear waves is found to be influenced by initial stress, interface imperfection and the presence of micropolarity in the elastic half space. The theoretical results obtained are useful for the design of high performance surface acoustic devices.

• Journal of electromagnetic engineering and science
• /
• v.19 no.2
• /
• pp.71-81
• /
• 2019

This paper presents a design methodology for wideband single-layered microwave absorbers with arbitrary absorption at the design center frequency using reactive Salisbury screens. The bandwidth of the absorber increases when the flatness of the reflection response at the design center frequency is maximized. Based on this observation, closed-form design formulas for wideband absorbers are derived. As they are scalable to any design frequency, wideband reactive screens can be systematically realized using two-dimensional periodic crossed-dipole structures patterned on a resistive sheet. Based on this method, a single-layered absorber with a 90% bandwidth improved to 124% of the design center frequency is presented. For the purpose of physical demonstration, an absorber with a design center frequency of 10 GHz is designed and fabricated using a silver nanowire resistive film with a surface resistance of 30 Ω/square. The measured absorption shows a good agreement with both the calculation and the electromagnetic simulation.

• Advances in nano research
• /
• v.12 no.4
• /
• pp.427-440
• /
• 2022

In the present study, the nonlocal strain gradient theory is used to predict the size-dependent buckling and post-buckling behavior of geometrically imperfect nano-scale piezo-flexomagnetic plate strips in two modes of direct and converse flexomagnetic effects. The first-order shear deformation plate theory is used to analyze analytically nano-strips with simply supported boundary conditions. The nonlinear governing equations of equilibrium and associated boundary conditions are derived using the principle of minimum total potential energy with consideration of the von Kármán-type of geometric nonlinearity. A closed-form solution of governing differential equation is obtained, which is easily usable for engineers and designers. To validate the presented formulations, whenever possible, a comparison with the results found in the open literature is reported for buckling loads. A parametric study is presented to examine the effect of scaling parameters, plate slenderness ratio, temperature, the mid-plane initial rise, flexomagnetic coefficient, different temperature distributions, and magnetic potential, in case of the converse flexomagnetic effect, on buckling and post-buckling loads in detail.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.26 no.1
• /
• pp.50-55
• /
• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

• Advances in Computational Design
• /
• v.5 no.1
• /
• pp.55-89
• /
• 2020

For the first time, an accurate analytical solution, based on coupled three-dimensional (3D) piezoelasticity equations, is presented for free vibration analysis of the angle-ply elastic and piezoelectric flat laminated panels under arbitrary boundary conditions. The present analytical solution is applicable to composite, sandwich and hybrid panels having arbitrary angle-ply lay-up, material properties, and boundary conditions. The modified Hamiltons principle approach has been applied to derive the weak form of governing equations where stresses, displacements, electric potential, and electric displacement field variables are considered as primary variables. Thereafter, multi-term multi-field extended Kantorovich approach (MMEKM) is employed to transform the governing equation into two sets of algebraic-ordinary differential equations (ODEs), one along in-plane (x) and other along the thickness (z) direction, respectively. These ODEs are solved in closed-form manner, which ensures the same order of accuracy for all the variables (stresses, displacements, and electric variables) by satisfying the boundary and continuity equations in exact manners. A robust algorithm is developed for extracting the natural frequencies and mode shapes. The numerical results are reported for various configurations such as elastic panels, sandwich panels and piezoelectric panels under different sets of boundary conditions. The effect of ply-angle and thickness to span ratio (s) on the dynamic behavior of the panels are also investigated. The presented 3D analytical solution will be helpful in the assessment of various 1D theories and numerical methods.

• Progress in Superconductivity and Cryogenics
• /
• v.15 no.3
• /
• pp.40-48
• /
• 2013

Cryoablation device is a surgical instrument to produce the cooling effect to destroy detrimental biological tissue by utilizing low temperature around 110 K. Usually, this device has the concentrated cooling region, so that it is suitable for concentrated and thick target. Accordingly, it is hard to apply this device for the target which is distributed and thin target. In this study, the design procedure of a closed-loop cryoablation device with multiple J-T expansion part is developed for the treatment of incompetent of great saphenous vein. The developed cyoablation device is designed with the analysis of 1-dimensional (1-D) bio-heat equation. The energy balance is considered to determine the minimum mass flow rate of refrigerant for consecutive flow boiling to develop the uniform cooling temperature. Azeotropic mixed refrigerant R410A and zeotropic mixed refrigerant (MR) of R22 ($CHClF_2$) and R23 ($CHF_3$) are utilized as operating fluids of the developed cryoablation device to form the sufficient temperature and to verify the quality of the inside of cryoablation probe. The experimental results of R410A and the zeotropic MR show the temperature non-uniformity over the range are $244.8K{\pm}2.7K$ and $239.8K{\pm}4.7K$ respectively. The experimental results demonstrate that the probe experiences the consecutive flow boiling over the target range of 200 mm.