한국생산제조학회 학술지 영문 홈페이지
[ Article ]
Journal of the Korean Society of Manufacturing Technology Engineers - Vol. 27, No. 4, pp.329-338
ISSN: 2508-5107 (Online)
Print publication date 15 Aug 2018
Received 03 Apr 2018 Revised 01 Jun 2018 Accepted 03 Aug 2018
DOI: https://doi.org/10.7735/ksmte.2018.27.4.329

Topological Shape Optimization Scheme for Nonlinear Structures Based on Artificial Bee Colony Algorithm

Yong-Ho Kima ; Seog-Young Hana, *
aSchool of Mechanical Engineering, Hanyang University, 222 Wangsimni-ro, Seongdong-gu, Seoul 04763, Korea

Correspondence to: *Tel.: +82-2-2220-0456 Fax: +82-2-2220-2299 E-mail address: syhan@hanyang.ac.kr (Seog-Young Han).

Abstract

This paper suggests a topological shape optimization scheme for nonlinear structures considering geometrically, materially and both geometrically and materially nonlinear cases based on an artificial bee colony algorithm (ABCA). To perform a topological shape optimization of nonlinear problems, a variable called “Improved Boundary Element Indicator (IBEI)” is introduced to define the boundary elements in each iteration. Typical examples consider three kinds of nonlinear cases, and it can be verified that the IBEI is suitable for topological shape optimization for linear and nonlinear structures. It can then be found that the suggested method can naturally create holes in the structure without any initial holes or topological sensitivity, although only the boundary elements are optimized. Finally, we conclude that convergence rate of the suggested ABCA is improved to more than 60% of the discrete level set method (LSM) and 5% of the ABCA for topology optimization (except for the geometrically nonlinear case).

Keywords:

Artificial bee colony algorithm, Topological shape optimization, Nonlinear structures, Boundary elements

References

  • Sethian, J. A., Wiegmann, A., 2000, Structural Boundary Design via Level Set and Immersed Interface Methods, J. Comput. Phys., 163:2 489-528.
  • Bourdin, B., Chambolle, A., 2003, Design-dependent Loads in Topology Optimization, ESAIM: Control, Optim. Calc. Var., 9 19-48. [https://doi.org/10.1051/cocv:2002070]
  • Allaire, G., Jouve, F., Toader, A.-M., 2004, Structural Optimization Using Sensitivity Analysis and a Level-set Method, J. Comput. Phys., 194:1 363-393.
  • Allaire, G., Jouve, F., 2008, Minimum Stress Optimal Design with the Level Set Method, Eng. Anal. Bound. Elem., 32:11 909-918.
  • Zhou, S., Wang, M. Y., 2007, Multimaterial Structural Topology Optimization with a Generalized Cahn–Hilliard Model of Multiphase Transition, Struct. Multidiscip. Optim., 33:2 89-111.
  • Takezawa, A., Nishiwaki, S., Kitamura, M., 2010, Shape and Topology Optimization Based on the Phase Field Method and Sensitivity Analysis, J. Comput. Phys., 229:7 2697-2718.
  • Behrou, R., Lawry, M., Maute, K., 2017, Level Set Topology Optimization of Structural Problems with Interface Cohesion, Int. J. Nemer. Method Eng., 112:8 990-1016.
  • Huang, X., Xie, Y. M., 2010, Evolutionary Topology Optimization of Continuum Structures: Methods and Applications, John Wiley & Sons, Chichester, United Kingdom. [https://doi.org/10.1002/9780470689486]
  • Kwak, J., Cho, S., 2005, Topological Shape Optimization of Geometrically Nonlinear Structures Using Level Set Method, Comput. Struct., 83:27 2257-2268.
  • Cho, S., Ha, S. H., Kim, M. G., 2006, Level Set Based Shape Optimization of Geometrically Nonlinear Structures, IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials, 217-226. [https://doi.org/10.1007/1-4020-4752-5_22]
  • Ha, S.-H., Cho, S., 2008, Level Set Based Topological Shape Optimization of Geometrically Nonlinear Structures Using Unstructured Mesh, Comput. Struct., 86:13-14 1447-1455.
  • Penzler, P., Rumpf, M., Wirth, B., 2012, A Phase-field Model for Compliance Shape Optimization in Nonlinear Elasticity, ESAIM: Control, Optim. Calc. Var., 18:1 229-258.
  • Myśliński, A., Koniarski, K., 2014, Phase Field Regularized Level Set Approach in Topology Optimization of Variational Inequalities, Methods and Models in Automation and Robotics (MMAR), 2014 19th International Conference on, 514-519.
  • Karaboga, D., Basturk, B., 2008, On the Performance of Artificial Bee Colony (ABC) Algorithm, Appl. Soft Comput., 8:1 687-697.
  • Storn, R., Price, K., 1997, Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, J. Glob. Optim., 11:4 341-359.
  • Kennedy, J., Eberhart, R., 1995, Particle Swarm Optimization, Neural Networks, Proceedings, IEEE International Conference on, 1942-1948.
  • Bäck, T., 1996, Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press.
  • Çavdar, T., Mohammad, M., Milani, R. A., 2013, A New Heuristic Approach for Inverse Kinematics of Robot Arms, Adv. Sci. Lett., 19:1 329-333.
  • Apalak, M. K., Karaboga, D., Akay, B., 2014, The Artificial Bee Colony Algorithm in Layer Optimization for the Maximum Fundamental Frequency of Symmetrical Laminated Composite Plates, Eng. Optim., 46:3 420-437.
  • Kim, Y.-H., Han, S.-Y., 2014, A Shape Optimization Scheme for Static Stiffness Problems, Proceedings of the International Conference of Manufacturing Technology Engineers (ICMTE) 2014, 183.
  • Kim, Y.-H., Han, S.-Y., 2015, A Shape Optimization Procedure Based on the Artificial Bee Colony Algorithm, Int. J. Precis. Eng. Manuf., 16:8 1825-1831.
  • Park, J.-Y., Han, S.-Y., 2013, Swarm Intelligence Topology Optimization Based on Artificial Bee Colony Algorithm, Int. J. Precis. Eng. Manuf., 14:1 115-121.
  • Park, J.-Y., Han, S.-Y., 2015, Topology Optimization for Nonlinear Structural Problems Based on Artificial Bee Colony Algorithm, Int. J. Precis. Eng. Manuf., 16:1 91-97.
  • Park, J.-Y., Han, S.-Y., 2013, Application of Artificial Bee Colony Algorithm to Topology Optimization for Dynamic Stiffness Problems, Comput. Math. Appl., 66:10 1879-1891.
  • Challis, V. J., 2010, A Discrete Level-set Topology Optimization Code Written in Matlab, Struct. Multidiscip. Optim., 41:3 453-464.
  • Kaveh, A., Hassani, B., Shojaee, S., Tavakkoli, S. M., 2008, Structural Topology Optimization Using Ant Colony Methodology, Eng. Struct., 30:9 2559-2565.