• 항공우주시스템공학회지
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• 제7권4호
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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.

• International Journal of Aeronautical and Space Sciences
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• 제8권1호
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• pp.95-104
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• 2007

A new design approach of complex geometries such as wing/body configuration is arranged by using overset mesh techniques under large scale computing environment. For an in-depth study of the flow physics and highly accurate design, several special overlapped structured blocks such as collar grid, tip-cap grid, and etc. which are commonly used in refined drag prediction are adopted to consider the applicability of the present design tools to practical problems. Various pre- and post-processing techniques for overset flow analysis and sensitivity analysis are devised or implemented to resolve overset mesh techniques into the design optimization problem based on Gradient Based Optimization Method (GBOM). In the pre-processing, the convergence characteristics of the flow solver and sensitivity analysis are improved by overlap optimization method. Moreover, a new post-processing method, Spline-Boundary Intersecting Grid (S-BIG) scheme, is proposed by considering the ratio of cell area for more refined prediction of aerodynamic coefficients and efficient evaluation of their sensitivities under parallel computing environment. With respect to the sensitivity analysis, discrete adjoint formulations for overset boundary conditions are derived by a full hand-differentiation. A smooth geometric modification on the overlapped surface boundaries and evaluation of grid sensitivities can be performed by mapping from planform coordinate to the surface meshes with Hicks-Henne function. Careful design works for the drag minimization problems of a transonic wing and a wing/body configuration are performed by using the newly-developed and -applied overset mesh techniques. The results from design applications demonstrate the capability of the present design approach successfully.

• 대한수학회논문집
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• 제26권1호
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• pp.37-49
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• 2011

We investigate the asymptotic equivalence for linear differential systems by means of the notions of $t_{\infty}$-similarity and strong stability.

• 대한수학회지
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• 제58권5호
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• 한국전산구조공학회논문집
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• 제28권1호
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• pp.9-18
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• 2015

본 논문에서는 애조인 설계민감도(DSA)를 사용하여 평형상태의 열전도문제에서 수치적으로 얻어진 위상 최적설계를 실험적으로 검증하였다. 애조인 변수법을 이용하면 해석에서 사용되었던 행렬시스템을 애조인 문제를 풀 때 그대로 활용가능하기 때문에 설계민감도를 얻는데 필요한 계산을 매우 효율적으로 수행할 수 있다. 위상 최적설계를 위해서 설계변수는 정규화된 재료밀도 함수로 정하였다. 목적함수는 구조물의 열 컴플라이언스이고 제한조건은 허용 가능한 재료량이다. 또한 열화상카메라를 활용하여 이러한 위상 최적설계로 얻어진 수치적 결과를 부피가 동일하도록 직관적으로 설계된 디자인과 비교하여 실험적으로 검증하였다. 위상 최적설계로 얻어진 결과를 실제로 제작하기 위해 간단한 수치기법을 통해 점 정보로 변환한 후 역설계 상용프로그램을 이용하여 CAD 모델링을 수행한다. 이를 바탕으로 위상 최적설계 결과를 CNC(Computerized Numerically Controlled machine tools) 선반으로 제작하였다.

• Journal of Mechanical Science and Technology
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• 제16권8호
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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.

• 대한기계학회논문집
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• 제15권6호
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• pp.1852-1860
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• 1991

본 연구에서는 연구대상을 주어진 구조물 형상에서 경계조건의 변화에 따른 현상 설계민감도, 특히 하중경계조건의 변화에 따른 구조물의 변형에 주안점을 두었다. 이 연구결과는 가공물의 지지위치에 따른 가공면의 변형정도 향상 및 접촉문제 해석등 에 응용이 가능하다. 유도된 민감도가 정확함을 입증하기 위하여 예제로서 하중경계 조건의 변화에 따른 범함수로 정의된 변형의 변화량을 예측하는 문제를 선정하였다.

• Journal of Mechanical Science and Technology
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• 제14권2호
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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.

• 수산해양기술연구
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• 제34권3호
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• pp.328-338
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• 1998

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 oder 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, where as 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 codes whose element derivative matrices can be explicitly generated. The numerical results of two cases - 2-dimensional portal frame and 3/4-cylindrical shell structure - for the deterministic and stochastic sensitivity analysis illustrates in this paper.

• Structural Engineering and Mechanics
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• 제56권5호
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• pp.871-897
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• 2015

This paper presents a novel method based on sensitivity of structural response for identifying both the system parameters and input excitation force of a bridge. This method, referred to as "Adjoint Variable Method", is a sensitivity-based finite element model updating method. The computational cost of sensitivity analyses is the main concern associated with damage detection by these methods. The main advantage of proposed method is inclusion of an analytical method to augment the accuracy and speed of the solution. The reliable performance of the method to precisely indentify the location and intensity of all types of predetermined single, multiple and random damages over the whole domain of moving vehicle speed is shown. A comparison study is also carried out to demonstrate the relative effectiveness and upgraded performance of the proposed method in comparison to the similar ordinary sensitivity analysis methods. Moreover, various sources of error including the effects of noise and primary errors on the numerical stability of the proposed method are discussed.