• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.127-134
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• 2004

In this paper, using an adjoint variable method, we develop a design sensitivity analysis (DSA) method applicable to heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume, respectively. Through several numerical examples, the developed DSA method is verified to yield very accurate sensitivity results compared with finite difference ones, requiring less than 0.3% of CPU time far the finite differencing. Also, the topology optimization yields physical meaningful results.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2005년도 춘계 학술발표회 논문집
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• pp.327-334
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• 2005

In this paper, using an adjoint variable method, we develop a design sensitivity analysis (DSA) method applicable to 3-Dimensional heat conduction problems in steady state. Also, a topology design optimization method is developed using the developed DSA method. Design sensitivity expressions with respect to the thermal conductivity are derived. Since the already factorized system matrix is utilized to obtain the adjoint solution, the cost for the sensitivity computation is trivial. For the topology design optimization, the design variables are parameterized into normalized bulk material densities. The objective function and constraint are the thermal compliance of structures and allowable material volume, respectively, Through several numerical examples, the developed DSA method is verified to yield efficiency and accurate sensitivity results compared with finite difference ones. Also, the topology optimization yields physical meaningful results.

• 수산해양기술연구
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• 제35권4호
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• pp.435-447
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• 1999

It is main objective of this approach to present a method to analyse stochastic design sensitivity for problems of structural dynamics with randomness in design parameters. A combination of the adjoint variable approach and the second order perturbation method is used in the finite element approach. An alternative form of the constant functional that holds for all times is introduced to consider the time response of dynamic sensitivity. The terminal problem of the adjoint system is solved using equivalent homogeneous equations excited by initial velocities. The numerical procedures are shown to be much more efficient when based on the fold superposition method: the generalized co-ordinates are normalized and the correlated random variables are transformed to uncorrelated variables, whereas the secularities are eliminated by the fast Fourier transform of complex valued sequences. Numerical algorithms have been worked out and proved to be accurate and efficient : they can be readily adapted to fit into the existing finite element codes whose element derivative matrices can be explicitly generated. The numerical results of two cases -2 dimensional portal frame for the comparison with reference and 3-dimensional frame structure - for the deterministic sensitivity analysis are presented.

• Computers and Concrete
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• 제7권1호
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• pp.63-81
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• 2010

We present the shape determination method of 3-D reinforcement corrosion based on observed temperature on concrete surface. The non-destructive testing for reinforcement corrosion in concrete using a heat image on concrete surface have been proposed by Oshita. The position of the reinforcement of corrosion or the cavity can be found using that method. However, the size of those defects can not be precisely measured based on the heat image. We therefore proposed the numerical determination system of the shape for the reinforcement corrosion using the observed temperature on the concrete surface. The adjoint variable method is introduced to formulate the shape determination problem, and the finite element method is employed to simulate the heat transfer problem. Some numerical experiments and the examination for the number of the observation points are shown in this paper.

• 대한기계학회논문집
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• 제18권1호
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• pp.12-23
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• 1994

This paper proposes an optimal design software for the open-chain dynamic systems whose governing equations are expressed as differential equation. In this software, an input module and an automatic creation module of the equation of motion are developed to contrive the user's convenience. To analyze the equation of motion of the dynamic systems, variable-order and variable-stepsize Adams-Bashforth-Moulton predictor-corrector method is used to improve the efficiency. For the optimization and the design sensitivity analysis, ALM(augmented lagrange multiplier)method and adjoint variable method are adopted respectively. An output module with which the user can compare and investigate the analysis and the optimization results through tables and graphs is also provided. The developed software is applied to three typical dynamic response optimization problems, and the results compare very well with those available in the literature, demonstrating its effectiveness.

• 한국정밀공학회지
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• 제20권8호
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• pp.175-184
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• 2003

A method of the shape design sensitivity analysis based on the boundary integral equation formulation is presented for two-dimensional inhomogeneous thermal conducting solids with multiple domains. Shape variation of the external and interface boundary is considered. A sensitivity formula of a general performance functional is derived by taking the material derivative to the boundary integral identity and by introducing an adjoint system. In numerical analysis, state variables of the primal and adjoint systems are solved by the boundary element method using quadratic elements. Two numerical examples of a compound cylinder and a thermal diffuser are taken to show implementation of the shape design sensitivity analysis. Accuracy of the present method is verified by comparing analyzed sensitivities with those by the finite difference. As application to the shape optimization, an optimal shape of the thermal diffuser is found by incorporating the sensitivity analysis algorithm in an optimization program.

• 한국전산유체공학회:학술대회논문집
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• 한국전산유체공학회 2006년도 추계 학술대회논문집
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• pp.208-208
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• 2006

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권2호
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• pp.161-166
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• 1997

We obtained sufficient conditions for $\phi$(t)-stability and uniform $\phi$(t)-stability of the trivial solution of comparison differential system. we also investigated the corresponding stability concepts of the trivial solution of the differential system using the thoery of differential inequlities through cones and the method of conevalued Lyapunov functions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.255-275
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• 2022

In this paper, we introduce a new system of set-valued variational inclusion problems in semi-inner product spaces. We use resolvent operator technique to propose an iterative algorithm for computing the approximate solution of the system of set-valued variational inclusion problems. The results presented in this paper generalize, improve and unify many previously known results in the literature.

• 소음진동
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• 제6권1호
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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.