• Journal of the Korea Institute of Information and Communication Engineering
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• v.20 no.8
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• pp.1487-1493
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• 2016

The susceptible, exposed, infectious, and recovered model (SEIR) is used extensively in the field of epidemiology. On the other hand, dissemination information among users through internet grows exponentially. This information spreading can be modeled as an epidemic. In this paper, we derive the mathematical model of SEIR in viral communication from the view of optimal control theory. Overall the methods based on classical calculus, In order to solve the optimal control problem, proved to be more efficient and accurate. According to Pontryagin's minimum principle (PMP) the Hamiltonian function must be optimized by the control variables at all points along the solution trajectory. We present our method based on the PMP and forward backward algorithm. In this algorithm, one should integrate forward in time for the state equations then integrate backward in time for the adjoint equations resulting from the optimality conditions. The problem is mathematically analyzed and numerically solved as well.

• Journal of Mechanical Science and Technology
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• v.16 no.8
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• pp.1102-1108
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• 2002

In this study, a topological design sensitivity of the ai. bearing surface (ABS) is suggested by using an adjoint variable method. The discrete form of the generalized lubrication equation based on a control volume formulation is used as a compatible condition. A residual function of the slider is considered as an equality constraint function, which represents the slider in equilibrium. The slider thickness parameters at all grid cells are chosen as design variables since they are the topological parameters determining the ABS shape. Then, a complicated adjoint variable equation is formulated to directly handle the highly nonlinear and asymmetric coefficient matrix and vector in the discrete system equation of air-lubricated slider bearings. An alternating direction implicit (ADI) scheme is utilized for the numerical calculation. This is an efficient iterative solver to solve large-scale problem in special band storage. Then, a computer program is developed and applied to a slider model of a sophisticated shape. The simulation results of design sensitivity analysis (DSA) are directly compared with those of FDM at the randomly selected grid cells to show the effectiveness of the proposed approach. The overall distribution of DSA results are reported, clearly showing the region on the ABS where special attention should be given during the manufacturing process.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.4
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• pp.9-14
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• 1985

In this research mass of a plane strain two dimensional elastic concrete dam under gravitational and hydrostatic loads is minimized, through shape optimization of the dam cross section. Cross sectional area of the dam is taken as cost function of the optimization problem while constraints on the principal stress distribution and dam thickness are imposed. Shape of the boundary of the model is chosen as design variable. Variational formulation of the optimization problem, the material derivative idea of continuum mechanics, and an adjoint variable method are employed for the shape design sensitivity calculation. Then the gradient projection algorithm is utilized to obtain an optimum design iteratively. Research results fully demonstrate that the theory and procedure adopted are quite efficient and can be applicable to a wide class of practical elastic structural design problems.

• Journal of Mechanical Science and Technology
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• v.14 no.2
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• pp.197-206
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• 2000

A boundary integral equation method in the shape design sensitivity analysis is developed for the elasticity problems with axisymmetric non-homogeneous bodies. Functionals involving displacements and tractions at the zonal interface are considered. Sensitivity formula in terms of the interface shape variation is then derived by taking derivative of the boundary integral identity. Adjoint problem is defined such that displacement and traction discontinuity is imposed at the interface. Analytic example for a compound cylinder is taken to show the validity of the derived sensitivity formula. In the numerical implementation, solutions at the interface for the primal and adjoint system are used for the sensitivity. While the BEM is a natural tool for the solution, more generalization should be made since it should handle the jump conditions at the interface. Accuracy of the sensitivity is evaluated numerically by the same compound cylinder problem. The endosseous implant-bone interface problem is considered next as a practical application, in which the stress value is of great importance for successful osseointegration at the interface. As a preliminary step, a simple model with tapered cylinder is considered in this paper. Numerical accuracy is shown to be excellent which promises that the method can be used as an efficient and reliable tool in the optimization procedure for the implant design. Though only the axisymmetric problem is considered here, the method can be applied to general elasticity problems having interface.

• Journal of KSNVE
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• v.6 no.1
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• pp.71-82
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• 1996

The finite element analysis for rotor bearing systems has been an essential tool for design, identification, and diagnosis of rotating machinery. Among others, the unbalance response analysis is fundamental in the vibration analysis of rotor bearing systems because rotating unbalance is recognized as a common sourve of vibration in rotating machinery. However there still remains a problem in the aspect of computational efficiency for unbalance response analysis of large rotor bearing systems. Gyroscopic terms and local bearing parameters in rotor bearing systems often make matters worse in unbalance response computation due to the complicated dynamic properties such as rotational speed dependency and/or anisotropy. The present paper proposes an efficient method for unbalance responses of multi-span rotor bearing systems. An improved substructure synthesis scheme is introduced which makes it possible to compute unbalance responses of the system by coupling unbalance responses of substructures that are of self adjoint problem with small order matrices. The present paper also suggests a scheme to easily deal with gyroscopic tems and local, coupling or bearing parameters. The proposed method causes no errors even though the computational effort is reduced drastically. The present method is demonstrated through three test examples.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.28 no.1
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• pp.9-18
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• 2015

In this paper, we verify the optimal topology design for heat conduction problems in steady stated which is obtained numerically using the adjoint design sensitivity analysis(DSA) method. In adjoint variable method(AVM), the already factorized system matrix is utilized to obtain the adjoint solution so that its computation cost is trivial for the sensitivity. For the topology optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of the structure and the allowable volume, respectively. For the experimental validation of the optimal topology design, we compare the results with those that have identical volume but designed intuitively using a thermal imaging camera. To manufacture the optimal design, we apply a simple numerical method to convert it into point cloud data and perform CAD modeling using commercial reverse engineering software. Based on the CAD model, we manufacture the optimal topology design by CNC.

• Proceedings of the KIEE Conference
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• 2011.07a
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• pp.872-873
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• 2011

This paper presents a multi-domain topology optimization using the harmonically excited coil and the iron in order to focus pulsed magnetic field (PMF). The design sensitivity of the harmonic magnetic field is derived by adjoint variable method. As a result of the optimization, PMF is considerably concentrated on the objective domain with much less leakage than the initial model.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.405-435
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• 2017

We deal with a sensitivity analysis of an optimal shape control problem for the stationary Navier-Stokes system. A two-dimensional channel flow of an incompressible, viscous fluid is examined to determine the shape of a bump on a part of the boundary that minimizes the viscous drag. By using the material derivative method and adjoint variables for a shape sensitivity analysis, we derive the shape gradient of the design functional for the model problem.

• Journal of Aerospace System Engineering
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• v.7 no.4
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• pp.27-35
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• 2013

Identifying the stability of rotor systems is prerequisite for clear determination of the parameter identification and safety, through which operating conditions may be rationally ascertained. For this purpose, the complex modal analysis of periodically time-varying system has been introduced by transforming the relation between periodic eigen-vectors and the corresponding adjoint vectors into the latent value problem. Stability investigation associated with modal features for rotor systems is performed using numerical simulation based upon the analysis model.

• Journal of the Korean Mathematical Society
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• v.52 no.3
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• pp.469-487
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• 2015

We consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indicate that hybrid on-off therapy protocols can move the model system to a "healthy" steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.