• 대한기계학회논문집A
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• 제26권12호
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• pp.2631-2635
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• 2002

The semi-analytic sensitivity analysis using Pade approximation is presented for linear elastic structures. Although the semi-analytic method has several advantages, accuracy of the method prevents it from practical application. One of promising remedies is the use of geometric series for the matrix inversion. Though series expansion of order three has been successfully applied to the calculation of the structural sensitivity in the most range of the design perturbation, it is prone to have a slow convergence for large perturbation. To overcome this shortage, Pade approximation is introduced so that it can broaden the trust region of the perturbation without adding expansion terms. Numerical results show that the confident sensitivity can be obtained with tiny expenses of computation effort.

• 대한기계학회논문집A
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• 제27권4호
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• 대한기계학회논문집A
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• 제27권2호
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• pp.262-267
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• 2003

Error of the geometric series expansion method for the structural sensitivity analysis is estimated. Although the semi-analytic method has several advantages, accuracy of the method prevents it from practical application. One of the promising remedies is the use of geometric series formula for the matrix inversion. Its result of the sensitivity analysis converges that of the global difference method which is known as reliable one. To reduce computational efforts and to obtain reliable results, it is important to know how many terms need to expand. In this paper, the error formula is presented and Its usefulness is illustrated through numerical experiments.

• 대한기계학회논문집A
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• 제27권4호
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• pp.585-592
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• 2003

Among various sensitivity evaluation techniques, semi-analytical method(SAM) is quite popular since this method is more advantageous than analytical method(AM) and global finite difference method(FDM). However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified fur individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, an iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes and the error of SAM caused by numerical difference scheme is alleviated by using a Von Neumann series approximation considering the higher order terms for the sensitivity derivatives.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집A
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• pp.686-691
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• 2001

Structural optimization often require the evaluation of design sensitivities. The Semi Analytic method(SAM) is popular for shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements, the SA method shows severe inaccuracy. In this paper, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover, the error of the SA method caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.491-496
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• 2003

In sensitivity analysis, semi-analytical method(SAM) reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Recently such errors of SAM resulted by the finite difference scheme have been improved by the separation of rigid body mode. But the eigenvalue should be obtained first before the sensitivity analysis is performed and it takes much time in the case that large system is considered. In the present study, by constructing a reduced one from the original system, iterative method combined with mode decomposition technique is proposed to compute reliable semi-analytical design sensitivities. The sensitivity analysis is performed by the eigenvector acquired from the reduced system. The error of SAM caused by difference scheme is alleviated by Von Neumann series approximation.

• 대한기계학회논문집
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• 제17권1호
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• pp.11-20
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• 1993

본 연구에서는 준 해석적 방법에 촛점을 맞추어 전개를 하려 한다. 대개의 최적설계방식이 그렇듯 준 해석적 방법도 치수변수에 관해 응용이 이루어졌는데 그 정 확도에 문제가 나타나지는 않는다. 그러나 최근 형상변수에 대해 응용을 할 경우 오 차가 큰 것이 발견되었다. 물론 치수변수에 관해서도 준 해석적 방법에서 오차가 존 재한다는 보고 있으나 그 절대량이 크지 않으므로 그다지 심각하지 않다고 사료된다. 여기서는 준해석적 방법의 오차의 과정이 수학적으로 전개될 것이며, 설정된 구조물에 대한 수치적 계산결과가 논의 될 것이다. 해석의 대상 구조물로는 엄밀해가 존재하 여 비교분석이 용이한 2차원 외팔보가 선택되었으며, 여러가지 방법과의 비교로서 준 해석적 방법이 논의되고 효과적인 방법선택이 제안될 것이다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.418-423
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• 2008

Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

• 대한기계학회논문집A
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• 제33권3호
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• pp.243-250
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• 2009

The adjoint variable method can reduce computation time and save computer resources because it can selectively provide the sensitivity information for the positions that designers wish to measure. However, the adjoint variable method commonly employs exact analytical differentiation with respect to the design variables. It can be cumbersome to precisely differentiate every given type of finite element. This trouble can be overcome only if the numerical differentiation scheme can replace this exact manner of differentiation. But, the numerical differentiation scheme causes of severe inaccuracy due to the perturbation size dilemma. For assuring the accurate sensitivity without any dependency of perturbation size, this paper employs a complex variable that has been mainly used for computational fluid dynamics problems. The adjoint variable method combined with complex variables is applied to obtain the shape and size sensitivity for structural optimization. Numerical examples demonstrate that the proposed method can predict stable sensitivity results and that its accuracy is remarkably superior to traditional sensitivity evaluation methods.

• 대한기계학회논문집A
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• 제33권8호
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• pp.745-752
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• 2009

In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.