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http://dx.doi.org/10.3795/KSME-A.2003.27.4.585

A Refined Semi-Analytic Sensitivity Study Based on the Mode Decomposition and Neumann Series Expansion (I) - Static Problem -  

Cho, Maeng-Hyo (서울대학교 기계항공공학부)
Kim, Hyun-Gi (서울대학교 기계항공공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers A / v.27, no.4, 2003 , pp. 585-592 More about this Journal
Abstract
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.
Keywords
Rigid Body Mode; Semi Analytic Method; Iterative Method; Perturbation Size; Eigenvalue Problem; Von Neumann Series;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Zienkiewicz O.C. and Campbell J.S., 1973, 'Shape Optimization and Sequential Linear Programming,' In: Gallgher RH, Zienkiewicz OC,editors. Optimum structural design. New York: Wiley, pp. 109-127
2 Barthelemy, B. and Haftka, R.T. 1990, 'Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity,' Mech.Struct.Mach., Vol. 18, pp. 407-432   DOI
3 Cheng, G. and Olhoff, N. 1993, 'Rigid Body Motion Test in Semi-Analytical Sensitivity Analysis,' Computers and Structures, Vol. 46(3), pp. 515-527   DOI   ScienceOn
4 Mlejnek, H.P., 1993, 'Accuracy of Semi-Analytical Sensitivities and Its Improvement by the Natural Method', Struct.Optim.,Vol. 4, pp. 128-131   DOI
5 De Boer, H. and Van Keulen, F. 2000, 'Refined Semi-Analytical Design Sensitivities,' Int.J.Solids Struct., Vol. 37, pp. 6961-6980   DOI   ScienceOn
6 Suha Oral, 1996, 'An Improved Semi-Analytical Method for Sensitivity Analysis,' Structural Optimization, Vol. 78, pp. 467-472
7 Cheng, G. and Liu, Y. 1987, 'A New Sensitivity Scheme for Sensitivity Analysis,' Engineering Optimization, Vol. 12, pp. 219-234   DOI
8 Kim, H. and Cho, M. 2001, 'A Study on the Improvement of Shape Desing Sensitivity in Eigenvalue Problems Using Semi-Analytical Method,' Proc.COSEIK Symposium-Fall, pp. 159-165
9 Cho, M. and Kim, H. 2002, 'A Refined Semi-Analytic Sensitivity Based on the Mode Decomposition and Neumann Series Expansion,' AIAA/ASME/ASCE/ AHS/ASC,43rd SDM Conference, pp. 2002-1738
10 Aminpour, M.A. 1992, 'An Assumed Stress Hybrid 4 Node Shell Element with Drilling Degrees of Freedom,' Int.J.Numer. Mech. Engng., Vol. 33, pp. 19-38   DOI
11 Kim, H. 2002, 'A Study of Refined Semi-Analytic Sensitivity Based on the Finite Element,' M.S.Thesis, Seoul National University
12 Van Keulen, F. and De Boer, H. 1998, 'Rigorous Improvement of Semi-Analytical Design Sensitivities by Exact Differentiation of Rigid Body Motions,' Int.J.Numer.Mech.Engng.,Vol. 42. pp. 71-91   DOI   ScienceOn
13 Suha Oral, 2000, 'A Mindlin Plate Finite Element with Semi-Analytical Shape Design Sensitivities,' Computers and Structures, Vol. 78, pp. 467-472   DOI   ScienceOn