Topology Optimization for Frequencies Using an Evolutionary Method
Publication: Journal of Structural Engineering
Volume 125, Issue 12
Abstract
This paper presents an evolutionary method for structural topology optimization subject to frequency constraints. The evolutionary structural optimization (ESO) method is based on the idea that by gradually removing inefficient material, the residual shape of structure evolves toward an optimum. The method is further developed by allowing the material to be added as well as removed, and this new approach is called the bidirectional ESO method (BESO). BESO has been successfully used for problems of stress and stiffness/displacement constraints. Its application to frequency optimization is addressed in this paper. Three kinds of optimization objectives, namely, maximizing a single frequency, maximizing multiple frequencies, and designing structures with prescribed frequencies are considered. Four examples are tested by BESO and ESO. The objective functions yielded by the two methods are close, and BESO is computationally more efficient in most cases.
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References
1.
Bartholomew, P., and Pitcher, N. (1984). “Optimization of structures with repeated normal-mode frequencies.” Engrg. Optim., 7, 195–208.
2.
Bendsøe, M. P., and Kikuchi, N. (1988). “Generating optimal topologies in structural design using a homogenization method.” Comput. Methods Appl. Mech. Engrg., 71, 197–224.
3.
Chapman, C. D., Saitou, K., and Jakiela, M. J. (1994). “Genetic algorithms as an approach to configuration and topology design.” Journal of Mechanical Design, 116, 1005–1012.
4.
Choi, K. K., Huang, E. J., and Seong, H. (1983). “An iterative method for finite dimensional structural optimization problems with repeated eigenvalues.” Int. J. Numer. Methods in Engrg., 19(1), 93–112.
5.
Díaz, A. R., and Kikuchi, N. (1992). “Solution to shape and topology eigenvalue optimization problems using a homogenization method.” Int. J. Numer. Methods in Engrg., 35, 1478–1502.
6.
Ding, Y. (1986). “Shape optimization of structures: A literature review.” Comp. and Struct., 24, 985–1004.
7.
Grandhi, R. (1993). “Structural optimization with frequency constraints—a review.” AIAA J., 31(12), 2296–2303.
8.
Hemp, W. S. (1973). Optimum structures. Clarendon Press, Oxford, U.K.
9.
Heyman, J. (1951). “Plastic design of beams and frames for minimum material consumption.” Quarterly of Applied Mathematics, 8, 373–381.
10.
Huang, M. W., and Arora, J. S. (1995). “Engineering optimization with discrete variables.” Proc., 36th AIAA/ASME/ASCE/AHS/ASC Struct., Struct. Dyn., and Mat. Conf., and AIAA/ASME Adaptive Struct. Forum (Part I), 1475–1483.
11.
Inou, N., Shimotai, N., and Uesugi, T. (1994). “A cellular automaton generation topological structures.” Proc., 2nd Euro. Conf. on Smart Struct. and Mat., 47–50.
12.
Kirkpatrick, S., Gelantt, C., and Vecchi, M. (1983). “Optimization by simulated annealing.” Science, 220, 671–680.
13.
Kirsch, U. (1989). “Optimal topologies of structures.” Appl. Mech. Rev., 42, 223–239.
14.
Ma, Z. D., Kikuchi, N., and Cheng, H. C. (1995). “Topology design for vibrating structures.” Comput. Methods Appl. Mech. Engrg., 121, 259–280.
15.
Mattheck, C. (1997). Design in nature: Learning from trees. Springer, Berlin.
16.
Michell, A. G. M. (1904). “The limits of economy in frame structures.” Phil. Mag., 8, 589–597.
17.
Prager, W., and Shield, R. T. (1968). “Optimal design of multi-purpose structures.” Int. J. Solids and Struct., 4, 469–475.
18.
Prager, W., and Rozvany, G. I. N. ( 1977). “Optimization of structural geometry.” Dynamic systems, A. R. Bednarek and L. Cesari, eds., Academic Press, New York, 265–293.
19.
Querin, O. M. ( 1997). “Evolutionary structural optimization: Stress-based formulation and implementation,” PhD thesis, The University of Sydney, Sydney, Australia.
20.
Querin, O. M., Young, V., Steven, G. P., and Xie, Y. M. (1998). “Computational efficiency and validation of bi-directional evolutionary structural optimization.” Proc., 4th World Congr. on Computat. Mech., Buenos Aires, Argentina.
21.
Tenek, L. H., and Hagiwara, I. (1993). “Static and vibrational shape and topology optimization using homogenization and mathematical programming.” Comput. Methods Appl. Mech. Engrg., 109, 143–154.
22.
Topping, B. H. V. ( 1993). “Topology design of discrete structures.” Topology design of structures, M. P. Bendsøe and C. A. Mota Soares, eds., Kluwer, Dordrecht, The Netherlands, 517–534.
23.
Venkayya, V. B., Khot, N. S., and Reddy, V. S. ( 1977). “Optimization of structures based on the study of strain energy distribution.” AFFDL-TR-68-150.
24.
Xie, Y. M., and Steven, G. P. (1997). Evolutionary structural optimization. Springer, Berlin.
25.
Yang, R. J., and Chuang, C. H. (1994). “Optimal topology design using linear programming.” Comput. and Struct., 52, 265–275.
26.
Yang, X. Y., Xie, Y. M., Steven, G. P., and Querin, O. M. (1999). “Bi-directional evolutionary method for stiffness optimization.” AIAA J., 37(11) (in press).
27.
Yang, X. Y. ( 1999). “Bi-directional evolutionary method for stiffness and displacement optimization,” ME thesis, School of the Built Environment, Victoria University of Technology, Victoria, Australia.
28.
Young, V., Querin, O. M., Steven, G. P., and Xie, Y. M. (1998). “3D bi-directional evolutionary structural optimization.” Proc., the Australiasian Conf. on Struct. Optimization, Sydney, Australia, 275–282.
29.
Zhou, M., and Rozvany, G. I. N. (1991). “The COC algorithm, Part II: Topological, geometry and generalized shape optimization.” Comput. Methods Appl. Mech. Engrg., 89, 197–224.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 125 • Issue 12 • December 1999
Pages: 1432 - 1438
History
Received: Sep 11, 1998
Published online: Dec 1, 1999
Published in print: Dec 1999
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