Topology Optimization for Frequencies Using an Evolutionary Method

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.

[1]  Y. Xie,et al.  Bidirectional Evolutionary Method for Stiffness Optimization , 1999 .

[2]  William Prager,et al.  Optimal design of multi-purpose structures* , 1968 .

[3]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[4]  V. B. Venkayya,et al.  Optimization of Structures Based on the Study of Energy Distribution , 1968 .

[5]  N. Kikuchi,et al.  Topological design for vibrating structures , 1995 .

[6]  Ren-Jye Yang,et al.  Optimal topology design using linear programming , 1994 .

[7]  A. Michell.  LVIII. The limits of economy of material in frame-structures , 1904 .

[8]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[9]  Yunliang Ding,et al.  Shape optimization of structures: a literature survey , 1986 .

[10]  J. Heyman.  Plastic design of beams and plane frames for minimum material consumption , 1951 .

[11]  B. H. V. Topping,et al.  Topology Design of Discrete Structures , 1993 .

[12]  Y. Xie,et al.  Computational efficiency and validation of bi-directional evolutionary structural optimisation , 2000 .

[13]  Claus Mattheck,et al.  Design in Nature: Learning from Trees , 1998 .

[14]  Kyung K. Choi,et al.  An iterative method for finite dimensional structural optimization problems with repeated eigenvalues , 1983 .

[15]  Min-Wei Huang,et al.  Engineering optimization with discrete variables , 1995 .

[16]  Kazuhiro Saitou,et al.  Genetic algorithms as an approach to configuration and topology design , 1994, DAC 1993.

[17]  Yi Min Xie,et al.  Evolutionary Structural Optimization , 1997 .

[18]  P. Bartholomew,et al.  OPTIMIZATION OF STRUCTURES WITH REPEATED NORMAL-MODE FREQUENCIES , 1984 .

[19]  Uri Kirsch,et al.  Optimal Topologies of Structures , 1989 .

[20]  Ramana V. Grandhi,et al.  Structural optimization with frequency constraints - A review , 1992 .

[21]  M. Zhou,et al.  The COC algorithm, Part II: Topological, geometrical and generalized shape optimization , 1991 .

[22]  N. Kikuchi,et al.  Solutions to shape and topology eigenvalue optimization problems using a homogenization method , 1992 .

[23]  Ichiro Hagiwara,et al.  Static and vibrational shape and topology optimization using homogenization and mathematical programming , 1993 .

[24]  G.I.N. Rozvany,et al.  OPTIMIZATION OF STRUCTURAL GEOMETRY , 1977 .