Efficient finite difference design sensitivities

AIAA Journal

Volumn 43, Issue 2, 2005, Pages 399-405

  Kirsch, Uri ^a,c   Bogomolni, Michael ^a,c   Van Keulen, Fred ^b,d  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

^b Koiter Institute Delft   (Netherlands)

^c Department of Civil Engineering ^*  (Israel)

^d Struct Optimization Compl M   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; EIGENVALUES AND EIGENFUNCTIONS; ERROR ANALYSIS; FINITE DIFFERENCE METHOD; LOADS (FORCES); MATRIX ALGEBRA; VECTORS;

DISPLACEMENTS; LOAD VECTORS; MASS MATRIX; VARIABLES;

SENSITIVITY ANALYSIS;

EID: 13444291952     PISSN: 00011452     EISSN: None     Source Type: Journal    
DOI: 10.2514/1.7855     Document Type: Article

References (18)

1. Haftka, R. T., and Gurdal, Z., Elements of Structural Optimization, 3rd ed., Kluwer Academic, Dordrecht, The Netherlands, 1993.
2. Barthelemy, B., Chon, C. T., and Haftka, R. T., "Sensitivity Approximation of Static Structural Response," Finite Element in Analysis and Design, Vol. 4, No. 3, 1988, pp. 249-265.
3. Pedersen, P., Cheng, G., and Rasmussen, J., "On Accuracy Problems for Semi-Analytical Sensitivity Analysis," Mechanics of Structures and Machines, Vol. 17, 1989, pp. 373-384.
4. Kirsch, U., Design-Oriented Analysis of Structures, Kluwer Academic, Dordrecht, The Netherlands, 2002.
5. Kirsch, U., "Effective Sensitivity Analysis for Structural Optimization," Computer Methods in Applied Mechanics and Engineering, Vol. 117, No. 1-2, 1994, pp. 143-156.
6. Kirsch, U., and Papalambros, P. Y., "Accurate Displacement Derivatives for Structural Optimization Using Approximate Reanalysis," Computer Methods in Applied Mechanics and Engineering, Vol. 190, No. 31, 2001, pp. 3945-3956.
7. Burton, R. R., "Computing Forward-Difference Derivatives in Engineering Optimization," Engineering Optimization, Vol. 20, No. 3, 1992, pp. 205-224.
8. Barthelemy, B., Chon, C. T., and Haftka, R. T., "Accuracy Analysis of the Semi-Analytical Method for Shape Sensitivity," Mechanics of Structures and Machines, Vol. 18, 1990, pp. 407-432.
9. Olhoff, N., and Rasmussen, J., "Study of Inaccuracy in Semi-Analytical Sensitivity Analysis - A Model Problem," Structural Optimization, Vol. 3, No. 4, 1991, pp. 203-213.
10. Cheng, Y., and Olhoff, N., "Rigid Body Motion Test Against Error in Semi-Analytical Sensitivity Analysis," Computers and Structures, Vol. 46, No. 3, 1993, pp. 515-527.
11. Mlejnek, H. P., "Accuracy of Semi-Analytical Sensitivities and Its Improvement by the Natural Method," Structural Optimization, Vol. 4, No. 2, 1992, pp. 128-131.
12. Van Keulen, F., and De Boer, H., "Rigorous Improvement of Semi-Analytical Design Sensitivities by Exact Differentiation of Rigid Body Motions," International Journal for Numerical Methods in Engineering, Vol. 42, No. 1, 1998, pp. 71-91.
13. Kirsch, U., and Liu, S., "Exact Structural Reanalysis by a First-Order Reduced Basis Approach," Structural Optimization, Vol. 10, No. 3, 1995, pp. 153-158.
14. Akgun, M. A., Garcelon, J. H., and Haftka, R. T., "Fast Exact Linear and Nonlinear Structural Reanalysis and the Sherman-Morrison-Woodbury Formulas," International Journal for Numerical Methods in Engineering, Vol. 50, No. 7, 2001, pp. 1587-1606.
15. Kirsch, U., and Papalambros, P. Y., "Exact and Accurate Solutions in the Approximate Reanalysis of Structures," AIAA Journal, Vol. 39, No. 11, 2001, pp. 2198-2205.
16. Bathe, K. J., Finite Element Procedures, Prentice-Hall, Upper Saddle River, NJ, 1996.
17. Kirsch, U., "Approximate Vibration Reanalysis of Structures," AIAA Journal, Vol. 41, No. 3, 2003, pp. 504-511.
18. Kirsch, U., and Bogomolni, M., "Procedures for Approximate Eigen-problem Reanalysis of Structures," International Journal for Numerical Methods in Engineering, Vol. 60, 2004, pp. 1969-1986.