Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-24T00:22:35.805Z Has data issue: false hasContentIssue false
  • English
  • Français

Optimal Shape/Topological Design of Plate/Shell Like Structures Subjected to Periodic Excitations

Published online by Cambridge University Press:  05 May 2011

Hsien-Chie Cheng  and
Kuo-Ning Chiang
Hsien-Chie Cheng*
Affiliation:
Computational Solid Mechanics Laboratory, Research and Promotion Division, National Center for High-Performance Computing, Hsinchu, Taiwan 300, R.O.C.
Kuo-Ning Chiang*
Affiliation:
Computational Solid Mechanics Laboratory, Research and Promotion Division, National Center for High-Performance Computing, Hsinchu, Taiwan 300, R.O.C.
*
*Associate Research Scientist
**Research Scientist
Get access

Abstract

This paper deals with the optimal shape/topological design of plate/shell like structures subjected to a harmonic, periodic excitation using an improved Homogenization Based Optimization Algorithm (HBOA), proposed by Cheng et al., [7]. The major goal of this work is to improve or control the frequency response of structures via the optimal distribution of a given amount of material in a fixed design space. Based upon the improved HBOA, two types of frequency response optimization problems are extensively explored: (1) structures subjected to a periodic excitation with a single excitation frequency, (2) structures subjected to a periodic excitation with excitation frequencies in a frequency domain. To this end, the basic mathematical formulation and a solution method are proposed as well as two numerical examples of obtaining the optimum layout of three-dimensional plate/shell structures. An interesting result is reported from the current optimization problems in comparison with static optimization problems.

Keywords

Shape/topology optimizationFrequency response problemsOptimal design of plate/shell like structuresHomogenization method
Type
Articles
Information
Journal of Mechanics , Volume 14 , Issue 1 , March 1998 , pp. 41 - 48
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 1998

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Olhoff, N. and Rozvany, G. I. N., “Optimal Grillage Layout for Given Natural Frequency,” J. Struc. Mech, ASCE, 108, pp. 971–974 (1982).Google Scholar
2.Bendsoe, M. P. and Kikuchi, N., “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Comput. Meth. Appl. Mech. Engng., 71, pp. 197–224 (1988).CrossRefGoogle Scholar
3.Diaz, A. R. and Kikuchi, N., “Solutions to Shape and Topology Eigenvalue Optimization Problems Using a Homogenization Method,” Int. J. Num. Meth. Engng., 35, pp. 1487–1502 (1992).CrossRefGoogle Scholar
4.Ma, Z. D., Kikuchi, N., and Hagiwara, I., “Structural Topology and Shape Optimization for a Frequency Response Problem,” Computational Mechanics, 13, pp. 157–174(1993).CrossRefGoogle Scholar
5.Ma, Z. D., Cheng, H. C, Kikuchi, N., and Hagiwara, I., “Topology and Shape Optimization Technique for Structural Dynamic Problems,” J. Applied Mechs., ASME, Vol. 62, pp. 200–207 (1995).CrossRefGoogle Scholar
6.Ma, Z. D., Cheng, H.-C. and Kikuchi, N., “Structural Design for Obtaining Desired Frequencies by Using the Topology and Shape Optimization Method,” Compng Sysm. Engng, Vol. 5, No. 1, pp. 77–89(1994).Google Scholar
7.Cheng, H. C, Kikuchi, N., and Ma, Z. D., “Generalized Shape/Topology Designs of Plate/Shell Structures for Eigenvalue Optimization Problems,” 20r/z ASME Design Automation Conference (1994).Google Scholar
8.Suzuki, K. and Kikuchi, N., “Generalized Layout Optimization of Three–Dimensional Shell Structures,” in Field, D. A. and Komokov, V., Geometric Aspects of Industrial Design, SIAM, pp. 62–88(1992).Google Scholar
9.Guedes, J. M. and Kikuchi, N., “Preprocessing and Postprocessing for Materials Based on the Homogenization Method with Adaptive Finite Element Methods,” Comp. Meth. Appl. Mechs. Engng., 83, pp. 143–198 (1990).CrossRefGoogle Scholar
10.Lions, J. L., “Some Methods in the Mathematical Analyses of Systems and Their Control,” Science Press, Beijing, China, Gordon and Breach, New York (1981).Google Scholar
11.Cheng, K. T. and Olhoff, N., “An Investigation Concerning Optimal Design of Solid Elastic Plates,” Int. J. Solids and Structures, 17, pp. 305–323 (1981).CrossRefGoogle Scholar
12.Rozvany, G. I. N., Zhou, M., Birker, T., and Sigmund, O., “Topology Optimization Using Iterative Continuum-Type Optimality Criteria Methods for Discretized Systems,” in Bendsoe, M. P. and Soates, C. A. M. (ed): Topology Design of Structures, NATO ASI Series (KluwerAcademic), pp. 273–286.Google Scholar
13.Cheng, H. C, Kikuchi, N., and Ma, Z. D., “An Improved Approach for Determining the Optimal Orientation of the Orthotropic Material,” Structural Optimization, Vol. 8, pp. 101–112 (1994).CrossRefGoogle Scholar