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The Semi-Analytic Structural Sensitivity Using Pade Approximation

Pade근사를 이용한 준해석 구조 민감도의 해석

  • 단호진 (한국과학기술원 기계공학과) ;
  • 이병채 (한국과학기술원 기계공학과)
  • Published : 2002.12.01

Abstract

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.

Keywords

References

  1. Bartherlemy, B., Chon, C. T. and Haftka, R. T., 1988. 'Accuracy Problems Associated with Semi-Analytic Derivatives of Static Response,' Finite Elements in Analysis and Design, Vol. 4, pp. 249-265 https://doi.org/10.1016/0168-874X(88)90011-X
  2. Cheng, G., Gu, Y. and Zhou, Y., 1989, 'Accuracy of Semi-Analytic Sensitivity Analysis,' Finite Elements in Analysis and Design, Vol. 6, pp. 113-128 https://doi.org/10.1016/0168-874X(89)90039-5
  3. Keulen, F. V. and Boer, H. De, 1998, 'Rigorous Improvement of Semi-Analytical Design Sensitivities by Exact Differentiation of Rigid Body Motions,' International Journal for Numerical Methdos in Engineering, Vol. 42, pp. 71-91 https://doi.org/10.1002/(SICI)1097-0207(19980515)42:1<71::AID-NME350>3.0.CO;2-C
  4. Oral, S., 2000, 'A Mindlin Plate Finite Element with Semi-Analytical Shape Design Sensitivities,' Computers & Structures, Vol. 78, pp. 467-472 https://doi.org/10.1016/S0045-7949(00)00068-7
  5. Chen, S. H., Yang, X. W., and Wu, B. S., 2000, 'Static Displacement Reanalysis of Structures Using Perturbation and Pade Approximation,' Communications in Numerical Methods in Engineering, Vol. 16, pp. 75-82 https://doi.org/10.1002/(SICI)1099-0887(200002)16:2<75::AID-CNM308>3.0.CO;2-X
  6. Maron, M. J. and Lopez, R. J., 1991, Numerical Analysis: A Practical Approach, 3rd ED., Wadsworth, Inc., USA, pp. 579-584
  7. Jeyachandrabose, C., Kirkhope, J. and Babu, C. R., 1985, 'An Alternative Explicit Formulation for the DKT Plate-Bending Element,' International Journal for Numerical Methods in Engineering, Vol. 21, pp. 1289-1293 https://doi.org/10.1002/nme.1620210709