Shape-Size Optimization of Plane Trusses with Designer's Preference
Publication: Journal of Structural Engineering
Volume 124, Issue 11
Abstract
This paper describes a new method for shape and member-size optimization of a plane truss by using techniques of parametric curves. Description of nodal coordinates as well as cross-sectional areas in terms of Bézier curves enables one to find a smooth optimal truss. The optimal truss is found under the constraints such that all the response strains to multiple design loads including static loads and earthquake excitation are within a prescribed range. The objective function to be minimized is a weighted sum of the total structural mass and the deviation of the shape from the one preferred by the designer. The latter is written explicitly in terms of the coordinates of the control points. Side constraints are easily incorporated based on the convex hull property of the Bézier curve. In the examples, optimal trusses are found under single and multiple loading conditions and the characteristics of the optimal trusses in reference to the weight coefficients are discussed.
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References
1.
Arora, J. S., and Tseng, C. H. (1987). IDESIGN user's manual ver. 3.5. Optimal Design Laboratory, University of Iowa, Iowa City, Iowa.
2.
Barnhill, R. E., and Boehm, W., eds. (1982). Surfaces in computer aided geometric design. North-Holland, Amsterdam, The Netherlands.
3.
Belegundu, A. D., and Arora, J. S.(1984). “A recursive quadratic programming method with active set strategy for optimal design.”Int. J. Numer. Methods in Engrg., 20, 803–816.
4.
Braibant, V., and Fleury, C.(1984). “Shape optimal design using B-splines.”Computational Methods of Appl. Mech. and Engrg., 44, 247–267.
5.
Eschenauer, H. A., Kobelev, V. V., and Schumacher, A.(1994). “Bubble method for topology and shape optimization of structures.”Struct. Optimization, 8, 42–51.
6.
Farin, G. (1988). Curves and surfaces for computer aided geometric design. Academic Press, San Diego, Calif.
7.
Haug, E. J., Choi, K. K., and Komkov, V. (1986). Design sensitivity analysis of structural systems. Academic Press, Orlando, Fla.
8.
Lin, J. H., Che, W. Y., and Yu, Y. S.(1982). “Structural optimization on geometrical configuration and dynamical constraints.”Int. J. Comp. and Struct., 15(5), 507–515.
9.
Nakamura, T., and Ohsaki, M.(1989). “Sequential generator of earthquake-response constrained trusses for design strain ranges.”Comp. and Struct., 33(6), 1403–1416.
10.
Newmark, N. M., and Hall, W. J. (1982). Earthquake spectra and design. Earthquake Engineering Research Institute, Berkeley, Calif.
11.
Ohsaki, M., Nakamura, T., and Kohiyama, M.(1997). “Shape optimization of double-layer space trusses described by parametric surfaces.”Space Struct., 12(2), 109–119.
12.
Ohsaki, M., Uetani, K., and Takatani, S. (1996). “Shape-stress trade-off design method of membrane structures by using inverse problem approach.”J. Struct. Constr. Engrg., 488, 107–115 (in Japanese).
13.
Ramm, E., Bletzinger, K.-U., and Reitinger, R.(1993). “Shape optimization of shell structures.”Bull. Int. Assn. for Shell and Spatial Struct., 34(112), 103–121.
14.
Saka, M. P.(1980). “Shape optimization of trusses.”J. Struct. Div., ASCE, 106(5), 1155–1174.
15.
Semby, W., and Kiureghian, A. D.(1985). “Modal combination rules for multicomponent earthquake excitation.”Earthquake Engrg. and Struct. Dyn., 13, 1–12.
16.
Twu, S.-L., and Choi, K. K.(1992). “Configuration design sensitivity analysis of built-up structures. Part I: Theory.”Int. Numer. Methods in Engrg., 35, 1127–1150.
17.
Wilson, E. L., Kiureghian, A. D., and Bayo, E. P.(1982). “A replacement of the SRSS method in seismic analysis.”Earthquake Engrg. and Struct. Dyn., 13, 1–12.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 124 • Issue 11 • November 1998
Pages: 1323 - 1330
Copyright
Copyright © 1998 American Society of Civil Engineers.
History
Published online: Nov 1, 1998
Published in print: Nov 1998
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