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Topology optimization for nonlinear structural problems based on artificial bee colony algorithm

Abstract

Topology algorithm is suggested for nonlinear structural problems based on artificial bee colony algorithm (ABCA). Although ABCA has been successfully applied to static and dynamic stiffness topology optimizations, it has never been applied to nonlinear structural problems. In order to examine whether the topology algorithm is suitable for nonlinear problems, it is applied to geometrically nonlinear, materially nonlinear, and both geometrically nonlinear and materially nonlinear topology optimization. Waggle index update rule and changing filter scheme were implemented with ABCA to obtain a robust and stable optimized topology. Some examples were presented to show the applicability and effectiveness of the suggested algorithm and compared with solid isotropic material with penalization (SIMP). It was concluded that the proposed algorithm can be applied to the above three kinds of nonlinear structural problems and has been verified as effective and applicable topology algorithm.

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References

  1. 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, pp. 143–154, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  2. Bendsoe, M. P. and Sigmund, O., “Topology Optimization: Theory, Methods and Applications,” Springer, pp. 1–70, 2003.

    Google Scholar 

  3. Huang, X. and Xie, M., “Evolutionary Topology Optimization of Continuum Structures: Methods and Applications,” John Wiley & Sons, pp. 39–50, 121–150, 2010.

    Google Scholar 

  4. Madeira, J. A., Pina, H., and Rodrigues, H., “GA Topology Optimization using Random Keys for Tree Encoding of Structures,” Structural and Multidisciplinary Optimization, Vol. 40, No. 1–6, pp. 227–240, 2010.

    Article  MATH  Google Scholar 

  5. 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.

    Article  Google Scholar 

  6. Buhl, T., Pedersen, C. B., and Sigmund, O., “Stiffness Design of Geometrically Nonlinear Structures using Topology Optimization,” Structural and Multidisciplinary Optimization, Vol. 19, No. 2, pp. 93–104, 2000.

    Article  Google Scholar 

  7. Huang, X. and Xie, Y., “Topology Optimization of Nonlinear Structures under Displacement Loading,” Engineering Structures, Vol. 30, No. 7, pp. 2057–2068, 2008.

    Article  Google Scholar 

  8. Karaboga, D., “An Idea based on Honey Bee Swarm for Numerical optimization,” Erciyes University, Technical Report-TR06, 2005.

    Google Scholar 

  9. Kang, F., Li, J., and Xu, Q., “Structural Inverse Analysis by Hybrid Simplex Artificial Bee Colony Algorithms,” Computers & Structures, Vol. 87, No. 13, pp. 861–870, 2009.

    Article  Google Scholar 

  10. Park, J.-Y. and Han, S.-Y., “Swarm Intelligence Topology Optimization based on Artificial Bee Colony Algorithm,” Int. J. Precis. Eng. Manuf., Vol. 14, No. 1, pp. 115–121, 2013.

    Article  MathSciNet  Google Scholar 

  11. 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.

    Article  MathSciNet  Google Scholar 

  12. Karaboga, D. and Basturk, B., “On the Performance of Artificial Bee Colony (ABC) Algorithm,” Applied Soft Computing, Vol. 8, No. 1, pp. 687–697, 2008.

    Article  Google Scholar 

  13. 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.

    Article  MATH  MathSciNet  Google Scholar 

  14. Kaveh, A., Hassani, B., Shojaee, S., and Tavakkoli, S., “Structural Topology Optimization using Ant Colony Methodology,” Engineering Structures, Vol. 30, No. 9, pp. 2559–2565, 2008.

    Article  Google Scholar 

  15. Sigmund, O. and Petersson, J., “Numerical Instabilities in Topology Optimization: A Survey on Procedures Dealing with Checkerboards, Mesh-Dependencies and Local Minima,” Structural Optimization, Vol. 16, No. 1, pp. 68–75, 1998.

    Article  Google Scholar 

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Correspondence to Seog-Young Han.

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Park, JY., Han, SY. Topology optimization for nonlinear structural problems based on artificial bee colony algorithm. Int. J. Precis. Eng. Manuf. 16, 91–97 (2015). https://doi.org/10.1007/s12541-015-0011-7

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  • DOI: https://doi.org/10.1007/s12541-015-0011-7

Keywords

  • Artificial bee colony algorithm (ABCA)
  • Fitness
  • Geometrically nonlinear
  • Materially nonlinear
  • Nonlinear structural problems
  • Waggle index