• Proceedings of the KIEE Conference
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• 2008.07a
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• pp.651-652
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• 2008

This research presents a multi-objective optimal design employing topological approach to maximize magnetic energy while minimizing structural deformation which is caused by magnetic reluctance force and magnetostriction. A design sensitivity formula is derived by employing the adjoint variable method (AVM) to avoid numerous sensitivity evaluations for a coupled magneto-mechanical analysis. The sensitivity analysis is verified using the finite difference method (FDM) in a C-shape actuator. A linear actuator used in a home appliance is examined for optimal design and demonstrates the strength of the proposed topology optimization approach.

• International Journal of Aeronautical and Space Sciences
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• v.2 no.1
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• pp.20-27
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• 2001

Aerodynamic sensitivity analysis is performed for the Navier-Stokes equations coupled with two-equation turbulence models using a discrete adjoint method and a direct differentiation method respectively. Like the mean flow equations, the turbulence model equations are also hand-differentiated to accurately calculate the sensitivity derivatives of flow quantities with respect to design variables in turbulent viscous flows. The sensitivity codes are then compared with the flow solver in terms of solution accuracy, computing time and computer memory requirements. The sensitivity derivatives obtained from the sensitivity codes with different turbulence models are compared with each other. The capability of the present sensitivity codes to treat complex geometry is successfully demonstrated by analyzing the flows over multi-element airfoils on Chimera overlaid grid systems.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.10a
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• pp.238-245
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• 2000

A general formulation for shape design sensitivity analysis over a plane arch structure is developed based on a variational formulation of curved beam in linear elasticity. Sensitivity formula is derived using the material derivative concept and adjoint variable method for the stress defined at a local segment. Obtained sensitivity expression, which can be computed by simple algebraic manipulation of the solution variables, is well suited for numerical implementation since it does not involve numerical differentiation. Due to the complete description for the shape and its variation of the arch, the formulation can manage more complex design problems with ease and gives better optimum design than before. Several examples are taken to show the advantage of the method, in which the accuracy of the sensitivity is evaluated. Shape optimization is also conducted with two design problems to illustrate the excellent applicability.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.32 no.10
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• pp.335-340
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• 1983

The analysis of static power converter circuit using state-space method is presented. Semiconductors are modeled in two-state resistors depending on their ON or OFF states. Then the modes of circuit are determined according to the conducting states of semiconductors and different describing matrices are given automatically for each mode. Newton-Raphson algorithm is used as an iterative method for obtaining steady-state solution and an adjoint network is introduced for the efficient and accurate evaluation of the Jacobi matrix in the algorithm. Using the porogram exploited from the above algorithm, it is shown through examples that the results are in good agreement with the analytic solutions and computation time is considerably reduced for obtaining the steady-state solutions.

• Proceedings of the KIEE Conference
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• summer
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• pp.770-772
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• 2004

This paper presents a new approach regarding thermal characteristics associated with a design of the high efficiency motor. The adjoint variable design sensitivity equations for both electromagnetics with respect to permeability and heat transfer considering conduction and convection terms are derived using the continuum method. For multi-objective topology optimization, FEA is validated in terms of electromagnetics and heat transfer by experiments. The proposed method is applied to a single-phase induction motor of the scroll compressor in order to control the direction of heat flow by maximizing/minimizing the temperature of the target area while maintaining the efficiency.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.4
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• pp.64-72
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• 1995

Sizing design sensitivity analysis of structures subjected to the harmonic vibration is performed using adjoint variable method. Constraint is the stress and sizing design variables are thickness, bending moment of inertia, and cross-sectional area of structures. Accurate sensitivities are computed and plotted sensitivity can be used as a design guidance tool. The accuracy of sensitivities is verified by the finite difference values. Also, optimal design of three-bar structure is performed using the computed sensitivity and feasible direction method while satisfying constraints and obtaining the minimum weight.

• 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.

• Structural Engineering and Mechanics
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• v.54 no.6
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• pp.1217-1244
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• 2015

In this research a theoretical and numerical study on a bridge damage detection procedure is presented based on vibration measurements collected from a set of accelerometers. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The approach relies on minimizing a penalty function, which usually consists of the errors between the measured quantities and the corresponding predictions attained from the model. Moving mass is an interactive model and includes inertia effects between the model and mass. This interactive model is a time varying system and the proposed method is capable of detecting damage in this variable system. Robustness of the proposed method is illustrated by correct detection of the location and extension of predetermined single, multiple and random damages in all ranges of speed and mass ratio of moving vehicle. A comparative study on common sensitivity and the proposed method confirms its efficiency and performance improvement in sensitivity-based damage detection methods. In addition various possible sources of error, including the effects of measurement noise and initial assumption error in stability of method are also discussed.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.1-10
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• 2009

This paper presents a topology optimization approach using element-free Galerkin method (EFGM) for the optimal design of compliant mechanisms with geometrically non-linearity. Meshless method has an advantage over the finite element method(FEM) because it is more capable of handling large deformation resulted from geometrical nonlinearity. Therefore, in this paper, EFGM is employed to discretize the governing equations and the bulk density field. The sensitivity analysis of the optimization problem is performed by incorporating the adjoint approach with the meshless method. The Lagrange multipliers method adjusted for imposition of both the concentrated and continuous essential boundary conditions in the EFGM is proposed in details. The optimization mathematical formulation is developed to convert the multi-criteria problem to an equivalent single-objective problem. The popularly applied interpolation scheme, solid isotropic material with penalization (SIMP), is used to indicate the dependence of material property upon on pseudo densities discretized to the integration points. A well studied numerical example has been applied to demonstrate the proposed approach works very well and the non-linear EFGM can obtain the better topologies than the linear EFGM to design large-displacement compliant mechanisms.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.5
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• pp.337-343
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• 2014

This paper presents a continuum-based shape design sensitivity analysis(DSA) method for crack propagation problems using a reproducing kernel method(RKM), which facilitates the remeshing problem required for finite element analysis(FEA) and provides the higher order shape functions by increasing the continuity of the kernel functions. A linear elasticity is considered to obtain the required stress field around the crack tip for the evaluation of J-integral. The sensitivity of displacement field and stress intensity factor(SIF) with respect to shape design variables are derived using a material derivative approach. For efficient computation of design sensitivity, an adjoint variable method is employed tather than the direct differentiation method. Through numerical examples, The mesh-free and the DSA methods show excellent agreement with finite difference results. The DSA results are further extended to a shape optimization of crack propagation problems to control the propagation path.