Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T14:05:36.881Z Has data issue: false hasContentIssue false
  • English
  • Français

Volume Adjustable Topology Optimization with Multiple Displacement Constraints

Published online by Cambridge University Press:  18 August 2017

C. W. Huang  and
K. W. Chou
C. W. Huang*
Affiliation:
Department of Civil EngineeringChung Yuan Christian UniversityTaoyuan, Taiwan
K. W. Chou
Affiliation:
National Center for Research on Earthquake EngineeringTaipei, Taiwan
*
*Corresponding author (cwhuang@cycu.edu.tw)
Get access

Abstract

Most topology optimization methods seek optimal topologies that satisfy a minimum compliance with a pre-specified volume constraint in the design domain. However, practical designs often include various functional constraints and the optimal solid volume ratios are unknown a priori, which implies a gap between topology optimization methods and practical designs in industries. This paper studies the performance-based topology optimization (PTO) problem that searches for the optimal topology with minimum compliance to satisfy the pre-specified functional constraints without a pre-specified volume constraint. A novel element-based evolutionary switching method (ESM), which can automatically adjust solid volume ratio and material distribution, is developed and implemented using the commercial finite element software ABAQUS. The effects of displacement constraints on the optimal topologies are investigated, and the differences between PTO problems and the topology optimization problem which has a volume constraint are discussed. Numerical examples demonstrate that the optimal topologies are mainly determined by the load pattern and locally changed with respect to the location of the active displacement constraints. In addition, the displacement constraints to a large extent control the solid volume ratio of optimal topologies according to the allowable displacements in PTO problems. Finally, the proposed ESM could provide conservative solutions to the topology optimization with multiple displacement constraints problems.

Keywords

Performance-based topology optimizationFunctional constraintsWithout volume constraintsEvolutionary switching method
Type
Research Article
Information
Journal of Mechanics , Volume 34 , Issue 6 , December 2018 , pp. 759 - 770
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2018 

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

1. Rozvancy, G. I. N., “Layout Theory for Grid-Type Structures,” Topology Design of Structures, Kluwer Academic Publishers, London, pp. 251–272 (1993).Google Scholar
2. Tanskanen, P., “The Evolutionary Structural Optimization Method: Theoretical Aspects,” Computer Methods in Applied Mechanics and Engineering, 191, pp. 5485–5498 (2002).Google Scholar
3. Bendsøe, M. P. and Kikuchi, N., “Generating Optimal Topologies in Structural Design Using a Homogenization Method,” Computer Methods in Applied Mechanics and Engineering, 71, pp. 197–224 (1988).Google Scholar
4. Suzuki, K. and Kikuchi, N., “A Homogenization Method for Shape and Topology Optimization,” Computer Methods in Applied Mechanics and Engineering, 93, pp. 291–318 (1991).Google Scholar
5. Bendsøe, M. P., “Optimal Shape Design as a Material Distribution Problem,” Structural Optimization, 1, pp. 193–202 (1989).Google Scholar
6. Mlejnek, H. P., “Some Aspects of the Genesis of Structures,” Structural Optimization, 5, pp. 49–64 (1992).Google Scholar
7. Bendsøe, M. P., Optimization of Structural Topology, Shape and Material, Springer, Berlin (1995).Google Scholar
8. Baumgartner, A., Harzheim, L. and Mattheck, C., “SKO (Soft Kill Option): the Biological Way to Find an Optimum Structure Topology,” International Journal of Fatigue, 14, pp. 387–393 (1992).Google Scholar
9. Xie, Y. M. and Steven, G. P., “A Simple Evolutionary Procedure for Structural Optimization,” Computers and Structures, 49, pp. 885–896 (1993).Google Scholar
10. Yang, X. Y., Xie, Y. M., Steven, G. P. and Querin, Q. M., “Bidirectional Evolutionary Method for Stiffness Optimization,” AIAA Journal, 37, pp. 1483–1488 (1999).Google Scholar
11. Huang, X. and Xie, Y. M., “Bi-Directional Evolutionary Topology Optimization of Continuum Structure with One or Multiple Material,” Computational Mechanics, 43, pp. 393–401 (2009).Google Scholar
12. Rouhi, M., Rais-Rohani, M. and Williams, T. N., “Element Exchange Method for Topology Optimization,” Structural and Multidisciplinary Optimization, 42, pp. 215–231 (2010).Google Scholar
13. Wang, M. Y., Wang, X. and Guo, D., “A Level Set Method for Structural Topology Optimization,” Computer Methods in Applied Mechanics and Engineering, 192, pp. 227–246 (2003).Google Scholar
14. Mei, Y. L. and Wang, X. M., “A Level Set Method for Structural Topology Optimization and Its Applications,” Advances in Engineering software, 35, pp. 415–441 (2004).Google Scholar
15. Amstutz, S. and Andrä, H., “A New Algorithm for Topology Optimization Using a Level-Set Method,” Journal of Computational Physics, 216, pp. 573–588 (2006).Google Scholar
16. Chu, D. N., Xie, Y. M., Hira, A. and Steven, G. P., “Evolutionary Structural Optimization for Problems with Stiffness Constraints,” Finite Element in Analysis and Design, 21, pp. 239–251 (1996).Google Scholar
17. Chu, D. N., Xie, Y. M., Hira, A. and Steven, G. P., “On Various Aspects of Evolutionary Structural Optimization for Problems with Stiffness Constraints,” Finite Element in Analysis and Design, 24, pp. 197–212 (1997).Google Scholar
18. Zhao, C., Steven, G. P. and Xie, Y. M., “Evolutionary Natural Frequency Optimization of Thin Plate Bending Vibration Problems,” Structural Optimization, 11, pp. 244–251 (1996).Google Scholar
19. Bendsøe, M. P. and Sigmund, O. Topology Optimization: Theory, Methods, and Applications, Springer, Berlin (2003).Google Scholar
20. Huang, X. and Xie, Y. M., “Evolutionary Topology Optimization of Continuum Structure with an Additional Displacement Constraint,” Structural and Multidisciplinary Optimization, 40, pp. 409–416 (2010).Google Scholar
21. Lin, C. Y. and Hsu, F. M., “An Adaptive Volume Constraint Algorithm for Topology Optimization with a Displacement-limit,” Advances in Engineering Software, 39, pp. 973–994 (2008).Google Scholar
22. Lin, C. Y. and Hsu, F. M., “Adaptive Volume Constraint Algorithm for Stress Limit-Based Topology Optimization,” Computer-Aided Design, 41, pp. 685–694 (2009).Google Scholar
23. Li, Q., Steven, G. P. and Xie, Y. M., “A Simple Checkerboard Suppression Algorithm for Evolutionary Structural Optimization,” Structural and Multidisciplinary Optimization, 22, pp. 230–239 (2001).Google Scholar
24. Abaqus User's Manual, Dassault Systèmes Simulia (2016).Google Scholar
25. Zuo, Z. H. and Xie, Y. M., “A Simple and Compact Python Code for Complex 3D Topology Optimization,” Advances in Engineering Software, 85, pp. 1–11 (2015).Google Scholar
26. Huang, X. and Xie, Y. M., “A Further Review of ESO Type Methods for Topology Optimization,” Structural and Multidisciplinary Optimization, 41, pp. 671–683 (2010).Google Scholar
27. Arora, J. S., Introduction to Optimum Design, 3rd edit., Academic Press, Boston (2011).Google Scholar