Abstract
The purpose of this study is to suggest a method of applying the artificial bee colony algorithm (ABCA) in the frequency topology optimization for a structure with multiple eigenfrequencies. In order to replicate the multiple eigenfrequencies of a structure, suboptimization procedure for multiple eigenfrequencies was additionally developed. In order to obtain a stable and robust optimal topology the waggle index update rule, evaluation method of fitness values and changing filtering size scheme were also employed. And the optimized topologies of ABCA for examples were compared with those of the solid isotropic material with penalization (SIMP) method for investigating the applicability and effectiveness of the ABCA. The following conclusions were obtained through the results of examples; (1) The ABCA implemented with sub-optimization procedure and the three suggested schemes, is very applicable and effective in dynamic topology optimization. (2) The multiple eigenfrequencies of a structure are successfully replicated by the ABCA in optimization procedure. (3) The fundamental frequency of the ABCA is almost the same or slightly higher than that of the SIMP
Similar content being viewed by others
References
Tenek, L. H. and Hagiwara, I., “Static and Vibrational Shape and Topology Optimization using Homogenization and Mathematical Programming,” Computer Methods in Applied Mechanics and Engineering, Vol. 109, No. 1–2, pp. 143–154, 1993.
Bendsøe, M. P. and Sigmund, O., “Topology Optimization: Theory, Methods and Applications,” Springer Science & Business Media, 2003.
Huang, X., Zuo, Z. H., and Xie, Y. M., “Evolutionary Topological Optimization of Vibrating Continuum Structures for Natural Frequencies,” Computers & Structures, Vol. 88, No. 5–6, pp. 357–364, 2010.
Alonso, C., Querin, O. M., and Ansola, R., “A Sequential Element Rejection and Admission (SERA) Method for Compliant Mechanisms Design,” Structural and Multidisciplinary Optimization, Vol. 47, No. 6, pp. 795–807, 2013.
Madeira, J. F. A., Pina, H. L., and Rodrigues, H. C., “Ga Topology Optimization using Random Keys for Tree Encoding of Structures,” Structural and Multidisciplinary Optimization, Vol. 40, No. 1–6, pp. 227–240, 2010.
Cui, G. Y., Tai, K., and Wang, B. P., “Topology Optimization for Maximum Natural Frequency using Simulated Annealing and Morphological Representation,” AIAA Journal, Vol. 40, No. 3, pp. 586–589, 2002.
Seyranian, A. P., Lund, E., and Olhoff, N., “Multiple Eigenvalues in Structural Optimization Problems,” Structural Optimization, Vol. 8, No. 4, pp. 207–227, 1994.
Du, J. and Olhoff, N., “Topological Design of Freely Vibrating Continuum Structures for Maximum Values of Simple and Multiple Eigenfrequencies and Frequency Gaps,” Structural and Multidisciplinary Optimization, Vol. 34, No. 2, pp. 91–110, 2007.
Lee, C.-y., Min, S., and Yoo, J., “Design of a Swing-Arm Actuator Using the Compliant Mechanism - Multi-Objective Optimal Design Considering the Stiffness Effect,” Transactions of the Korean Society of Mechanical Engineers A, Vol. 30, No. 2, pp. 128–134, 2006.
Karaboga, D., “An Idea based on Honey Bee Swarm for Numerical Optimization,” Technical Report-TR06, Erciyes University, Technical Report, No. TR06, 2005.
Karaboga, D. and Basturk, B., “A Powerful and Efficient Algorithm for Numerical Function Optimization: Artificial Bee Colony (ABC) Algorithm,” Journal of Global Optimization, Vol. 39, No. 3, pp. 459–471, 2007.
Karaboga, D. and Ozturk, C., “A Novel Clustering Approach: Artificial Bee Colony (ABC) Algorithm,” Applied Soft Computing, Vol. 11, No. 1, pp. 652–657, 2011.
Storn, R. and Price, K., “Differential Evolution–a Simple and Efficient Heuristic for Global Optimization Over Continuous Spaces,” Journal of Global Optimization, Vol. 11, No. 4, pp. 341–359, 1997.
Kennedy, J. and Eberhart, R. C., “Particle Swarm Optimization,” Proc. of IEEE International Conference on Neural Networks, Vol. 4, pp. 1942–1948, 1995.
Park, J. Y. and Han, S. Y., “Application of Artificial Bee Colony Algorithm to Topology Optimization for Dynamic Stiffness Problems,” Computers & Mathematics with Applications, Vol. 66, No. 10, pp. 1879–1891, 2013.
Huang, X., Zuo, Z. H., and Xie, Y. M., “Evolutionary Topological Optimization of Vibrating Continuum Structures for Natural Frequencies,” Computers & Structures, Vol. 88, No. 5–6, pp. 357–364, 2010.
Kaveh, A., Hassani, B., Shojaee, S., and Tavakkoli, S. M., “Structural Topology Optimization using Ant Colony Methodology,” Engineering Structures, Vol. 30, No. 9, pp. 2559–2565, 2008.
Svanberg, K., “The Method of Moving Asymptotes–A New Method for Structural Optimization,” International Journal for Numerical Methods in Engineering, Vol. 24, No. 2, pp. 359–373, 1987.
Svanberg, K., “A Class of Globally Convergent Optimization Methods based on Conservative Convex Separable Approximations,” SIAM Journal on Optimization, Vol. 12, No. 2, pp. 555–573, 2002.
Akay, B. and Karaboga, D., “A Modified Artificial Bee Colony Algorithm for Real-Parameter Optimization,” Information Sciences, Vol. 192, pp. 120–142, 2012.
Huang, X. and Xie, Y. M., “Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method,” Finite Elements in Analysis and Design, Vol. 43, No. 14, pp. 1039–1049, 2007.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chang, DH., Han, SY. Dynamic topology optimization for multiple eigenfrequencies using the artificial bee colony algorithm. Int. J. Precis. Eng. Manuf. 16, 1817–1824 (2015). https://doi.org/10.1007/s12541-015-0237-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12541-015-0237-4