Sensitivity of Optimum Designs for Spatially Varying Ground Motions
Publication: Journal of Structural Engineering
Volume 127, Issue 11
Abstract
An optimization method is presented for long-span frames for specified seismic responses considering spatial variation of ground motions. The response is evaluated by using a response spectrum approach, where incoherency effect, wave passage effect, and local amplification effect are considered. Sensitivity coefficients of the optimum objective value with respect to the parameters defining spatial variation of the seismic motions are computed based on the parametric programming method or postoptimal analysis. It is shown that the second-order parametric sensitivity coefficients are easily obtained if the first-order coefficients vanish due to symmetry and antisymmetry conditions of structure and ground motions. In the examples, optimum designs are found for an arch-type frame and the results of postoptimal analysis are verified in comparison with the parametric sensitivity coefficients by the central difference method. It is shown that the spatial variation of ground motions leads to the increase of the optimal structural volume under constraints on member strains.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abrahamson, N. A., Schneider, J. F., and Stepp, J. ( 1991). “Empirical spatial coherency functions for application to soil-structure interaction analysis.” Earthquake Spectra, 7(1), 1–28.
2.
Barthelemy, J., and Sobieszczanski-Sobieski, J. ( 1983). “Optimum sensitivity derivatives of objective functions in nonlinear programming.” AIAA J., 21(6), 913–915.
3.
Clough, R. W., and Penzien, J. ( 1975). Dynamics of structures, McGraw-Hill, New York.
4.
DebChaudhury, A., and Gazis, G. D. (1988). “Response of MDOF systems to multiple support seismic excitation.”J. Engrg. Mech., ASCE, 114(4), 583–603.
5.
Der Kiureghian, A. (1980). “Structural response to stationary excitation.”J. Engrg. Mech. Div., ASCE, 106(6), 1195–1213.
6.
Der Kiureghian, A. ( 1996). “A coherency model for spatially varying ground motions.” Earthquake Engrg. and Struct. Dynamics, 25(1), 99–111.
7.
Der Kiureghian, A., and Neuenhofer, A. ( 1991). “A response spectrum method for multiple-support seismic excitations.” Tech. Rep. No. UCB/EERC-91/08, Earthquake Engrg. Res. Ctr., University of California, Berkeley, Calif.
8.
Der Kiureghian, A., and Neuenhofer, A. ( 1992). “Response spectrum method for multiple-support seismic excitation.” Earthquake Engrg. and Struct. Dynamics, 21(8), 713–740.
9.
DOT user's manual ver. 5.0. (1999). Vanderplaats Research & Development Inc., Colorado Springs, Colo.
10.
Fiacco, A. V. ( 1983). Introduction to sensitivity and stability analysis in nonlinear programming, Academic, San Diego.
11.
Gal, T. ( 1979). Postoptimal analyses, parametric programming, and related topics, McGraw-Hill, New York.
12.
Guddat, J., Vasquez, F. G., and Jongen, H. T. ( 1990). Parametric optimization: Singularities, pathfollowing and jumps, Wiley, New York.
13.
Haftka, R. T., Gürdal, Z., and Kamat, M. P. ( 1990). Elements structural optimization, Kluwer Academic, Boston.
14.
Hao, H., and Duan, X. N. (1995). “Seismic response of asymmetric structures to multiple ground motions.”J. Struct. Engrg., ASCE, 121(11), 1557–1564.
15.
Harichandran, R. S., Hawwari, A., and Swedian, B. N. (1996). “Response of long-span bridges to spatially varying ground motion.”J. Struct. Engrg., ASCE, 122(5), 476–484.
16.
Haug, E. J., Choi, K. K., and Komkov, V. ( 1986). Design sensitivity analysis of structural systems, Academic, San Diego.
17.
Luco, J. E., and Wong, H. L. ( 1986). “Response of a rigid foundation to a spatially random ground motion.” Earthquake Engrg. and Struct. Dynamics, 14(6), 891–908.
18.
Nakamura, T., and Ohsaki, M. ( 1988). “Sequential optimal truss generator for frequency ranges.” Comput. Methods Appl. Mech. Engrg., 67(1), 189–209.
19.
Nakamura, T., and Ohsaki, M. ( 1989). “Sequential generator of earthquake-response constrained trusses for design strain ranges.” Comp. and Struct., 33(6), 1403–1416.
20.
Nakamura, T., and Ohsaki, M. ( 1992). “A natural generator of optimum topology of plane trusses for specified fundamental frequency.” Comput. Methods Appl. Mech. Engrg., 94(1), 113–129.
21.
Newmark, N. M., and Hall, W. J. ( 1982). “Earthquake spectra and design.” Tech. Rep., Earthquake Engineering Research Institute, Berkeley, Calif.
22.
Ohsaki, M., and Arora, J. S. ( 1993). “A direct application of higher order parametric programming techniques to structural optimization.” Int. J. Numer. Methods in Engrg., 36(16), 2683–2702.
23.
Ohsaki, M., Katoh, N., and Isshiki, Y. ( 1998a). “Interactive multiobjective two-level optimization of dissatisfaction level of structures.” Proc., 7th AIAA/USAF/NASA/ISSMO Symp. on Multidisciplinary Anal. and Optimization, American Institute of Aeronautics and Astronautics, Washington, D.C., 97–106.
24.
Ohsaki, M., Nakamura, T., and Isshiki, Y. (1998b). “Shape-size optimization of plane trusses with designer's preference.”J. Struct. Engrg., ASCE, 124(11), 1323–1330.
25.
Ohsaki, M., Tagawa, H., and Kato, Y. (2000). “Optimum design of structures subjected to spatially varying ground motion.”J. Struct. Engrg., AIJ, 46, 046B, 9–18 (in Japanese).
26.
Price, T. E., and Eberhard, M. O. (1998). “Effects of spatially varying ground motions on short bridges.”J. Struct. Engrg., ASCE, 124(8), 948–955.
27.
Vanderplaats, G., and Yoshida, N. ( 1985). “Efficient calculation of optimum design sensitivity.” AIAA J., 23(11), 1798–1803.
28.
Wilson, E. L., Der Kiureghian, A., and Bayo, E. P. ( 1980). “A replacement for the SRSS method in seismic analysis.” Earthquake Engrg. and Struct. Dynamics, 9(2), 187–194.
29.
Zembaty, Z. (1996). “Spatial seismic coefficients, some sensitivity results.”J. Engrg. Mech., ASCE, 122(4), 379–382.
30.
Zerva, A. ( 1990). “Response of multi-span beams to spatially incoherent seismic ground motions.” Earthquake Engrg. and Struct. Dynamics, 19(6), 819–832.
Information & Authors
Information
Published In
History
Received: Oct 3, 2000
Published online: Nov 1, 2001
Published in print: Nov 2001
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.