• Journal of the korean Society of Automotive Engineers
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• v.15 no.1
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• pp.81-88
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• 1993

A direct treatment of the min-max type objective function of the dynamic response optimization problem is proposed. Previously, the min-max type objective function was transformed to an artificial design variable and an additional point-wise state variable constraint function was imposed, which increased the complexity of the optimization problem. Especially, the design sensitivity analysis for the augmented Lagrangian functional with the suggested treatment is established by using the adjoint variable method and a computer program to implement the proposed algorithm is developed. The optimization result of the proposed treatment are obtained for three typical problems and compared with those of the previous treatment. It is concluded that the suggested treatment in much more efficient in the computational effort than the previous treatment with giving the similar optimal solutions.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.138-139
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• 2007

This research provides machine designers with some intuition to consider both, magnetic and heat transfer effects. A topological multi-objective function includes magnetic energy and heat inflow rate to the system, which equals to the total heat dissipation by conduction and convection. For the thermal field regarding the heat inflow, introduced as a reaction force, topology design sensitivity is derived by employing discrete equations. The adjoint variable method is used to avoid numerous sensitivity evaluations. As a numerical example, a C-core design excited by winding current demonstrates the strength of the multi-physical approach.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.

• Journal of KSNVE
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• v.8 no.2
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• pp.267-273
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• 1998

This study aims at performing sensitivity analysis of piezoelectric smart structure for minimizing radiated noise from the structure, The structure consists of a flat plate on which disk shaped piezoelectric actuator is mounted, and finite element modeling is used for the structure. The finite element modeling uses a combination of three dimensional piezoelectric, flat shell and transition elements so thus it can take into account the coupling effects of the piezoelectric device precisely and it can also reduce the degrees of freedom of the finite element model. Electric potential on the piezoelectric actuator is taken as a design variable and total radiated power of the structure is chosen as an objective function. The objective function can be represented as Rayleigh's integral equation and is a function of normal displacements of the structure. For the convenience of computation, all degrees of freedom of the finite element equation is condensed out except the normal displacements of the structure. To perform the design sensitivity analysis, the derivative of the objective function with respect to the normal displacements is found, and the derivative of the norma displacements with respect to the design variable is calculated from the finite element equation by using so called the adjoint variable method. The analysis results are compared with those of the finite difference method, and shows a good agreement. This sensitivity analysis is faster and more accurate than the finite difference method. Once the sensitivity analysis program is used for gradient-based optimizations, one could achieve a better convergence rate than non-derivative methods for optimal design of piezoelectric smart structures.

• 유체기계공업학회:학술대회논문집
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• 2006.08a
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• pp.33-36
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• 2006

As the computing environment is rapidly improved, the interests of CFD are gradually focused on large-scale computation over complex geometry. Keeping pace with the trend, essential computational tools to obtain solutions of complex aerospace flow analysis and design problems are examined. An accurate and efficient flow analysis and design codes for large-scale aerospace problem are presented in this work. With regard to original numerical schemes for flow analysis, high-fidelity flux schemes such as RoeM, AUSMPW+ and higher order interpolation schemes such as MLP (Multi-dimensional Limiting Process) are presented. Concerning the grid representation method, a general-purpose basis code which can handle multi-block system and overset grid system simultaneously is constructed. In respect to design optimization, the importance of turbulent sensitivity is investigated. And design tools to predict highly turbulent flows and its sensitivity accurately by fully differentiating turbulent transport equations are presented. Especially, a new sensitivity analysis treatment and geometric representation method to resolve the basic flow characteristics are presented. Exploiting these tools, the capability of the proposed approach to handle complex aerospace simulation and design problems is tested by computing several flow analysis and design problems.

• Computational Structural Engineering
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• v.7 no.2
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• pp.147-153
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• 1994

A method for shape design sensitivity analysis for axisymmetric shells of general shapes is developed. The basic approach is to divide the structures into many segments : For each of the segments, the formula for a shallow arch or shell can be applied and the results assembled. To interconnect those segments, the existing sensitivity formula, obtained for a variation only in the direction perpendicular to the plane on which the structure is mapped, has been extended to include a variation normal to the middle surface. The method follows the adjoint variable approach based on the material derivative concept as established in the literature. Numerical examples are taken to illustrate the method and the applicability to practical design problems.

• Nuclear Engineering and Technology
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• v.53 no.5
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• pp.1391-1402
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• 2021

The aim of this work is to prepare a neutron noise calculator based on the second order of average current nodal expansion method (ACNEM). Generally, nodal methods have the ability to fulfill the neutronic analysis with adequate precision using coarse meshes as large as a fuel assembly size. But, for the zeroth order of ACNEM, the accuracy of neutronic simulations may not be sufficient when coarse meshes are employed in the reactor core modeling. In this work, the capability of second order ACNEM is extended for solving the neutron diffusion equation in the frequency domain using coarse meshes. For this purpose, two problems are modeled and checked including a slab reactor and 2D BIBLIS PWR. For validating of results, a semi-analytical solution is utilized for 1D test case, and for 2D problem, the results of both forward and adjoint neutron noise calculations are exploited. Numerical results indicate that by increasing the order of method, the errors of frequency dependent coarse mesh solutions are considerably decreased in comparison to the reference. Accordingly, the accuracy of second order ACNEM can be acceptable for the neutron noise calculations by using coarse meshes in the nuclear reactor core.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.261-281
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• 2011

A new method of formulation of a class of elements that are immune to mesh distortion effects is proposed here. The simple three-noded bar element with an offset of the internal node from the element center is employed here to demonstrate the method and the principles on which it is founded upon. Using the function space approach, the modified formulation is shown here to be superior to the conventional isoparametric version of the element since it satisfies the completeness requirement as the metric formulation, and yet it is in agreement with the best-fit paradigm in both the metric and the parametric domains. Furthermore, the element error is limited to only those that are permissible by the classical projection theorem of strains and stresses. Unlike its conventional counterpart, the modified element is thus not prone to any errors from mesh distortion. The element formulation is symmetric and thus satisfies the requirement of the conservative nature of problems associated with all self-adjoint differential operators. The present paper indicates that a proper mapping set for distortion immune elements constitutes geometric and displacement interpolations through parametric and metric shape functions respectively, with the metric components in the displacement/strain replaced by the equivalent geometric interpolation in parametric co-ordinates.

• The Transactions of the Korean Institute of Electrical Engineers B
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• v.49 no.5
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• pp.327-337
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• 2000

In this paper, the design sensitivity formula for the control of the transient temperature distribution is developed using the direct differentiation method, and used for the optimal design of induction heating coil position. The temperature distribution is calculated using the heat source of the induced eddy current and heat diffusion equation. The physical property variations of the workpiece depending on the temperature are considered. The eddy current distribution and the temperature distribution are calculated with the 2D finite element procedure. The adjoint variable technique is employed in expressing the design sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region of the sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region sensitivity. The goal of the design is to have the desired distribution of the temperature on a specific region of the workpiece. The numerical example shows that the proposed design sensitivity analysis for the control of the transient temperature distribution is very useful and practical in the optimal design of induction heating coils.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.433-433
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• 2021

본 연구는 개수로 흐름에서 조류발전단지의 터빈 최적 배열의 거시적 특성에 관한 연구를 수행하였다. 천수방정식을 통해 직사각형 개수로의 흐름장을 해석하였고, 상류와 하류단에 대해 각각 유입경계조건(inlet boundary condition)과 Flather 형식의 개방경계조건(open boundary condition)을 부여하여 일정 유량으로 흐르는 개수로 흐름을 구현하였다. 더불어, Strickler의 법칙을 확장한 반력공식을 연계하여, 개수로 흐름에 대한 조류 터빈의 영향을 반영하였다. 주어진 상류의 흐름 조건에 대해 조류발전량을 최대로 하는 최적 배열을 구하기 위해 터빈 반력모형을 연계한 천수방정식, 터빈간 최소간격, 그리고 발전단지영역을 제한조건으로 하는 발전량 최대화 문제를 구성하였다. 여기서 조류 터빈의 위치를 나타내는 벡터를 설계변수로 두었는데, 설계되는 터빈의 수가 증가함에 따라 최적화 문제의 계산량이 증가하지 않도록 수반법(adjoint method)을 경사도기반법(gradient-based method)에 연계한 방법이 이용되었다. 다수의 터빈초기배치로 상당한 수치실험이 수행되었고, 발전량 최대화를 이루도록 최적화된 터빈의 배치들이 큰 규모에서 고유한 형상으로 수렴함을 확인하였다. 이러한 특성은 발전단지의 너비와 터빈의 최소간격의 함수로 정의된 무차원수 E를 바탕으로 설명되었다. 구체적으로, E가 1보다 작을 때에는 선형배열이 최적배열로 나타났고, E가 1을 넘어 점차 커짐에 따라 하류에 오목한 형상을 보이다가 V-형태로 발전하는 양상을 보였다. 또한, 어느 임계 수 이상의 터빈이 배치되는 경우 일열 배열을 유지하지 못하고 이열 배열로 분리됨이 관찰되었다.