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Investigating best algorithms for structural topology optimization

Year 2024, , 116 - 126, 19.01.2024
https://doi.org/10.31127/tuje.1298508

Abstract

This study investigates the topology optimization problem using various optimization approaches, taking inspiration from the 99-line MATLAB code developed by Sigmund. The educational MATLAB code is based on the Solid Isotropic Material with Penalization (SIMP) model of the artificial material density method. The objective is to minimize the compliance function with a weight constraint, with the design variables being the densities of all elements. The aim is to identify a more efficient optimization technique as an alternative to the commonly used optimality criteria algorithm provided by other MATLAB built-in tools. Two types of optimization algorithms are examined: gradient-based methods such as Interior-Point, Sequential Quadratic Programming (SQP), and Active-Set, as well as metaheuristic methods including the Genetic Algorithm. The results are verified and validated by comparing them with existing literature, demonstrating good agreement. Performance assessments are conducted to compare the results obtained from these algorithms in terms of quality and computational efficiency. The numerical findings indicate that the interior-point method outperforms the other investigated methods, although the optimality criteria algorithm remains the most efficient for solving topology optimization problems.

References

  • Deaton, J. D., & Grandhi, R. V. (2014). A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization, 49, 1-38. https://doi.org/10.1007/s00158-013-0956-z
  • Zargham, S., Ward, T. A., Ramli, R., & Badruddin, I. A. (2016). Topology optimization: a review for structural designs under vibration problems. Structural and Multidisciplinary Optimization, 53, 1157-1177. https://doi.org/10.1007/s00158-015-1370-5
  • Bendsøe, M. P. (1989). Optimal shape design as a material distribution problem. Structural optimization, 1, 193-202. https://doi.org/10.1007/BF01650949
  • Rozvany, G. I. (2009). A critical review of established methods of structural topology optimization. Structural and multidisciplinary optimization, 37, 217-237. https://doi.org/10.1007/s00158-007-0217-0
  • Bendsoe, M. P., & Sigmund, O. (2003). Topology optimization: theory, methods, and applications. Springer Science & Business Media.
  • Hassani, B., & Hinton, E. (1998). A review of homogenization and topology optimization I—homogenization theory for media with periodic structure. Computers & Structures, 69(6), 707-717. https://doi.org/10.1016/S0045-7949(98)00131-X
  • Eschenauer, H. A., & Olhoff, N. (2001). Topology optimization of continuum structures: a review. Applied Mechanics Reviews, 54(4), 331-390. https://doi.org/10.1115/1.1388075
  • Rozvany, G. I. N. (2001). Stress ratio and compliance-based methods in topology optimization–a critical review. Structural and Multidisciplinary Optimization, 21, 109-119. https://doi.org/10.1007/s001580050175
  • Tiismus, H., Kallaste, A., Vaimann, T., & Rassõlkin, A. (2022). State of the art of additively manufactured electromagnetic materials for topology optimized electrical machines. Additive Manufacturing, 55, 102778. https://doi.org/10.1016/j.addma.2022.102778
  • Cardillo, A., Cascini, G., Frillici, F. S., & Rotini, F. (2013). Multi-objective topology optimization through GA-based hybridization of partial solutions. Engineering with Computers, 29, 287-306. https://doi.org/10.1007/s00366-012-0272-z
  • Sivapuram, R., & Picelli, R. (2018). Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design, 139, 49-61. https://doi.org/10.1016/j.finel.2017.10.006
  • Talischi, C., Paulino, G. H., Pereira, A., & Menezes, I. F. (2012). PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Structural and Multidisciplinary Optimization, 45, 329-357. https://doi.org/10.1007/s00158-011-0696-x
  • Sigmund, O. (2001). A 99 line topology optimization code written in Matlab. Structural and multidisciplinary optimization, 21, 120-127. https://doi.org/10.1007/s001580050176
  • Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 43, 1-16. https://doi.org/10.1007/s00158-010-0594-7
  • Wang, S. Y., Tai, K., & Wang, M. Y. (2006). An enhanced genetic algorithm for structural topology optimization. International Journal for Numerical Methods in Engineering, 65(1), 18-44. https://doi.org/10.1002/nme.1435
  • Svanberg, K. (2002). A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal on Optimization, 12(2), 555-573. https://doi.org/10.1137/S1052623499362822
  • Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2), 359-373. https://doi.org/10.1002/nme.1620240207
  • Bendsøe, M. P., & Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 69, 635-654. https://doi.org/10.1007/s004190050248
  • Dantzig, G. B., & Thapa, M. N. (2003). Linear programming: Theory and extensions (Vol. 2). New York: Springer.
  • Jansen, B. (2013). Interior point techniques in optimization: Complementarity, sensitivity and algorithms (Vol. 6). Springer Science & Business Media.
  • Nocedal, J., & Wright, S. J. (Eds.). (1999). Numerical optimization. New York, NY: Springer New York.
  • Forsgren, A., Gill, P. E., & Wright, M. H. (2002). Interior methods for nonlinear optimization. SIAM Review, 44(4), 525-597. https://doi.org/10.1137/S0036144502414942
  • Dubois, T. (2013). EASA Requires A380 Structural Inspection for Cracking. https://www.ainonline.com/aviation-news/air-transport/2013-11-11/easa-requires-a380-structural-inspection-cracking
  • Singal, R. K., Gorman, D. J., & Forgues, S. A. (1992). A comprehensive analytical solution for free vibration of rectangular plates with classical edge coditions: Experimental verification. Experimental Mechanics, 32, 21-23. https://doi.org/10.1007/BF02317979
  • Hauser, F., Häberle, M., Merling, D., Lindner, S., Gurevich, V., Zeiger, F., Frank, R., & Menth, M. (2023). A survey on data plane programming with p4: Fundamentals, advances, and applied research. Journal of Network and Computer Applications, 212, 103561. https://doi.org/10.1016/j.jnca.2022.103561
  • Kramer, O. (2017). Genetic Algorithm Essentials, Springer International Publishing, Cham.
  • Kramer, O. (2017). Genetic algorithms (pp. 11-19). Springer International Publishing.
  • Madeira, J. A., Rodrigues, H. C., & Pina, H. (2006). Multiobjective topology optimization of structures using genetic algorithms with chromosome repairing. Structural and Multidisciplinary Optimization, 32, 31-39. https://doi.org/10.1007/s00158-006-0007-0
Year 2024, , 116 - 126, 19.01.2024
https://doi.org/10.31127/tuje.1298508

Abstract

References

  • Deaton, J. D., & Grandhi, R. V. (2014). A survey of structural and multidisciplinary continuum topology optimization: post 2000. Structural and Multidisciplinary Optimization, 49, 1-38. https://doi.org/10.1007/s00158-013-0956-z
  • Zargham, S., Ward, T. A., Ramli, R., & Badruddin, I. A. (2016). Topology optimization: a review for structural designs under vibration problems. Structural and Multidisciplinary Optimization, 53, 1157-1177. https://doi.org/10.1007/s00158-015-1370-5
  • Bendsøe, M. P. (1989). Optimal shape design as a material distribution problem. Structural optimization, 1, 193-202. https://doi.org/10.1007/BF01650949
  • Rozvany, G. I. (2009). A critical review of established methods of structural topology optimization. Structural and multidisciplinary optimization, 37, 217-237. https://doi.org/10.1007/s00158-007-0217-0
  • Bendsoe, M. P., & Sigmund, O. (2003). Topology optimization: theory, methods, and applications. Springer Science & Business Media.
  • Hassani, B., & Hinton, E. (1998). A review of homogenization and topology optimization I—homogenization theory for media with periodic structure. Computers & Structures, 69(6), 707-717. https://doi.org/10.1016/S0045-7949(98)00131-X
  • Eschenauer, H. A., & Olhoff, N. (2001). Topology optimization of continuum structures: a review. Applied Mechanics Reviews, 54(4), 331-390. https://doi.org/10.1115/1.1388075
  • Rozvany, G. I. N. (2001). Stress ratio and compliance-based methods in topology optimization–a critical review. Structural and Multidisciplinary Optimization, 21, 109-119. https://doi.org/10.1007/s001580050175
  • Tiismus, H., Kallaste, A., Vaimann, T., & Rassõlkin, A. (2022). State of the art of additively manufactured electromagnetic materials for topology optimized electrical machines. Additive Manufacturing, 55, 102778. https://doi.org/10.1016/j.addma.2022.102778
  • Cardillo, A., Cascini, G., Frillici, F. S., & Rotini, F. (2013). Multi-objective topology optimization through GA-based hybridization of partial solutions. Engineering with Computers, 29, 287-306. https://doi.org/10.1007/s00366-012-0272-z
  • Sivapuram, R., & Picelli, R. (2018). Topology optimization of binary structures using integer linear programming. Finite Elements in Analysis and Design, 139, 49-61. https://doi.org/10.1016/j.finel.2017.10.006
  • Talischi, C., Paulino, G. H., Pereira, A., & Menezes, I. F. (2012). PolyTop: a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes. Structural and Multidisciplinary Optimization, 45, 329-357. https://doi.org/10.1007/s00158-011-0696-x
  • Sigmund, O. (2001). A 99 line topology optimization code written in Matlab. Structural and multidisciplinary optimization, 21, 120-127. https://doi.org/10.1007/s001580050176
  • Andreassen, E., Clausen, A., Schevenels, M., Lazarov, B. S., & Sigmund, O. (2011). Efficient topology optimization in MATLAB using 88 lines of code. Structural and Multidisciplinary Optimization, 43, 1-16. https://doi.org/10.1007/s00158-010-0594-7
  • Wang, S. Y., Tai, K., & Wang, M. Y. (2006). An enhanced genetic algorithm for structural topology optimization. International Journal for Numerical Methods in Engineering, 65(1), 18-44. https://doi.org/10.1002/nme.1435
  • Svanberg, K. (2002). A class of globally convergent optimization methods based on conservative convex separable approximations. SIAM Journal on Optimization, 12(2), 555-573. https://doi.org/10.1137/S1052623499362822
  • Svanberg, K. (1987). The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24(2), 359-373. https://doi.org/10.1002/nme.1620240207
  • Bendsøe, M. P., & Sigmund, O. (1999). Material interpolation schemes in topology optimization. Archive of Applied Mechanics, 69, 635-654. https://doi.org/10.1007/s004190050248
  • Dantzig, G. B., & Thapa, M. N. (2003). Linear programming: Theory and extensions (Vol. 2). New York: Springer.
  • Jansen, B. (2013). Interior point techniques in optimization: Complementarity, sensitivity and algorithms (Vol. 6). Springer Science & Business Media.
  • Nocedal, J., & Wright, S. J. (Eds.). (1999). Numerical optimization. New York, NY: Springer New York.
  • Forsgren, A., Gill, P. E., & Wright, M. H. (2002). Interior methods for nonlinear optimization. SIAM Review, 44(4), 525-597. https://doi.org/10.1137/S0036144502414942
  • Dubois, T. (2013). EASA Requires A380 Structural Inspection for Cracking. https://www.ainonline.com/aviation-news/air-transport/2013-11-11/easa-requires-a380-structural-inspection-cracking
  • Singal, R. K., Gorman, D. J., & Forgues, S. A. (1992). A comprehensive analytical solution for free vibration of rectangular plates with classical edge coditions: Experimental verification. Experimental Mechanics, 32, 21-23. https://doi.org/10.1007/BF02317979
  • Hauser, F., Häberle, M., Merling, D., Lindner, S., Gurevich, V., Zeiger, F., Frank, R., & Menth, M. (2023). A survey on data plane programming with p4: Fundamentals, advances, and applied research. Journal of Network and Computer Applications, 212, 103561. https://doi.org/10.1016/j.jnca.2022.103561
  • Kramer, O. (2017). Genetic Algorithm Essentials, Springer International Publishing, Cham.
  • Kramer, O. (2017). Genetic algorithms (pp. 11-19). Springer International Publishing.
  • Madeira, J. A., Rodrigues, H. C., & Pina, H. (2006). Multiobjective topology optimization of structures using genetic algorithms with chromosome repairing. Structural and Multidisciplinary Optimization, 32, 31-39. https://doi.org/10.1007/s00158-006-0007-0
There are 28 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Sohayb Abdulkerim 0000-0002-3448-9129

Early Pub Date January 3, 2024
Publication Date January 19, 2024
Published in Issue Year 2024

Cite

APA Abdulkerim, S. (2024). Investigating best algorithms for structural topology optimization. Turkish Journal of Engineering, 8(1), 116-126. https://doi.org/10.31127/tuje.1298508
AMA Abdulkerim S. Investigating best algorithms for structural topology optimization. TUJE. January 2024;8(1):116-126. doi:10.31127/tuje.1298508
Chicago Abdulkerim, Sohayb. “Investigating Best Algorithms for Structural Topology Optimization”. Turkish Journal of Engineering 8, no. 1 (January 2024): 116-26. https://doi.org/10.31127/tuje.1298508.
EndNote Abdulkerim S (January 1, 2024) Investigating best algorithms for structural topology optimization. Turkish Journal of Engineering 8 1 116–126.
IEEE S. Abdulkerim, “Investigating best algorithms for structural topology optimization”, TUJE, vol. 8, no. 1, pp. 116–126, 2024, doi: 10.31127/tuje.1298508.
ISNAD Abdulkerim, Sohayb. “Investigating Best Algorithms for Structural Topology Optimization”. Turkish Journal of Engineering 8/1 (January 2024), 116-126. https://doi.org/10.31127/tuje.1298508.
JAMA Abdulkerim S. Investigating best algorithms for structural topology optimization. TUJE. 2024;8:116–126.
MLA Abdulkerim, Sohayb. “Investigating Best Algorithms for Structural Topology Optimization”. Turkish Journal of Engineering, vol. 8, no. 1, 2024, pp. 116-2, doi:10.31127/tuje.1298508.
Vancouver Abdulkerim S. Investigating best algorithms for structural topology optimization. TUJE. 2024;8(1):116-2.
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