Structural and Multidisciplinary Optimization

, Volume 58, Issue 2, pp 575–594 | Cite as

Truss topology optimization considering local buckling constraints and restrictions on intersection and overlap of bar members

  • Huiyong Cui
  • Haichao An
  • Hai Huang


This paper illustrates the application of a two-level approximation method for truss topology optimization with local member buckling constraints and restrictions on member intersections and overlaps. Previously developed for truss topology optimization with stress and displacement constraints, that method is achieved by starting from an initial ground structure, and, combined with genetic algorithm (GA), it can handle both discrete and continuous variables, which denote the existence and cross-sectional areas of bar members respectively in the ground structure. In this work, this method is improved and extended to consider member buckling constraints and restrict intersection and overlap of members for truss topology optimization. The temporary deletion technique is adopted to temporarily remove buckling constraints when related bar members are deleted, and in order to avoid unstable designs, the validity check for truss topology configuration is conducted. By using GA to search in each possible design subset, the singularity encountered in buckling-constrained problems is remedied, and meanwhile, as the required structural analysis is replaced with explicit approximation functions in the process of executing GA, the computational cost is significantly saved. Moreover, for the consideration of restrictions on member intersecting and overlapping, the definition of such phenomena and mathematical expressions to recognize them are presented, and a new fitness function is developed to include such considerations. Numerical examples are presented to show the efficacy of the proposed techniques.


Truss topology optimization Local buckling constraints Intersection and overlap Singular optima Two-level approximation Genetic algorithm 



This research work is supported by the National Natural Science Foundation of China (Grant No. 11672016), which the authors gratefully acknowledge.


  1. Achtziger W (1999a) Local stability of trusses in the context of topology optimization part I: exact modelling. Struct Optim 17(4):235–246Google Scholar
  2. Achtziger W (1999b) Local stability of trusses in the context of topology optimization part II: a numerical approach. Struct Multidiscip Optim 17(4):247–258MathSciNetGoogle Scholar
  3. Achtziger W (2000) Optimization with variable sets of constraints and an application to truss design. Comput Optim Appl 15(1):69–96MathSciNetCrossRefzbMATHGoogle Scholar
  4. An H, Chen S, Huang H (2015) Simultaneous optimization of stacking sequences and sizing with two-level approximations and a genetic algorithm. Compos Struct 123:180–189CrossRefGoogle Scholar
  5. An H, Huang H (2017) Topology and Sizing Optimization for Frame Structures with a Two-Level Approximation Method. AIAA J 55(3):1044–1057CrossRefGoogle Scholar
  6. An H, Xian K, Huang H (2016) Actuator placement optimization for adaptive trusses using a two-level multipoint approximation method. Struct Multidiscip Optim 53(1):29–48MathSciNetCrossRefGoogle Scholar
  7. Chen S, Lin Z, An H, Huang H, Kong C (2013) Stacking sequence optimization with genetic algorithm using a two-level approximation. Struct Multidiscip Optim 48(4):795–805MathSciNetCrossRefGoogle Scholar
  8. Chen S, Shui X, Huang H (2017) Improved genetic algorithm with two-level approximation using shape sensitivities for truss layout optimization. Struct Multidiscip Optim 55(4):1365–1382MathSciNetCrossRefGoogle Scholar
  9. Chen S, Shui X, Li D, Huang H (2015) Improved genetic algorithm with two-level approximation for truss optimization by using discrete shape variables. Math Probl Eng 2015(6):1–11MathSciNetGoogle Scholar
  10. Cheng G (1995) Some aspects of truss topology optimization. Struct Multidiscip Optim 10(3):173–179CrossRefGoogle Scholar
  11. Cheng G, Guo X (1997) ε-relaxed approach in structural topology optimization. Struct Multidiscip Optim 13(4):258–266CrossRefGoogle Scholar
  12. Cheng G, Guo X, Olhoff N (2000) New formulation for truss topology optimization problems under buckling constraints. Topology Optimization of Structures and Composite Continua. Kluwer Academic Publishers, In, pp 115–131Google Scholar
  13. Cheng G, Jiang Z (1992) Study on topology optimization with stress constraints. Eng Optim 20(2):129–148CrossRefGoogle Scholar
  14. Dong Y, Huang H (2004) Truss topology optimization by using multi-point approximation and GA. Chinese J Comput Mech 21(6):746–751MathSciNetGoogle Scholar
  15. Dorn WS (1964) Automatic design of optimal structures. Journal de Mecanique 3:25–52Google Scholar
  16. Guo X, Cheng G, Olhoff N (2005) Optimum design of truss topology under buckling constraints. Struct Multidiscip Optim 30(3):169–180CrossRefGoogle Scholar
  17. Guo X, Cheng G, Yamazaki K (2001) A new approach for the solution of singular optima in truss topology optimization with stress and local buckling constraints. Struct Multidiscip Optim 22(5):364–373CrossRefGoogle Scholar
  18. Hajela P, Lee E (1995) Genetic algorithms in truss topological optimization. Int J Solids Struct 32(22):3341–3357MathSciNetCrossRefzbMATHGoogle Scholar
  19. Kawamura H, Ohmori H, Kito N (2002) Truss topology optimization by a modified genetic algorithm. Struct Multidiscip Optim 23(6):467–473CrossRefGoogle Scholar
  20. Leng G, Qiu Y, Bao H (2012) Topology optimization of frame strcture based on intersection-filter. Engineering Mechanics 2:013Google Scholar
  21. Leng G, Zhang Z, Bao H, Yang D (2013) Topology optimization of truss structrue based on overlapping-filter and stability constraints. Engineering Mechanics 2:001Google Scholar
  22. Li D, Chen S, Huang H (2014) Improved genetic algorithm with two-level approximation for truss topology optimization. Struct Multidiscip Optim 49(5):795–814MathSciNetCrossRefGoogle Scholar
  23. Li J (2015) Truss topology optimization using an improved species-conserving genetic algorithm. Eng Optim 47(1):107–128MathSciNetCrossRefGoogle Scholar
  24. Li L, Khandelwal K (2017) Topology optimization of geometrically nonlinear trusses with spurious eigenmodes control. Eng Struct 131:324–344CrossRefGoogle Scholar
  25. Liu X, Cheng G, Yan J, Jiang L (2012) Singular optimum topology of skeletal structures with frequency constraints by AGGA. Struct Multidiscip Optim 45(3):451–466CrossRefGoogle Scholar
  26. Mela K (2014) Resolving issues with member buckling in truss topology optimization using a mixed variable approach. Struct Multidiscip Optim 50(6):1037–1049MathSciNetCrossRefGoogle Scholar
  27. Nocedal J, Wright SJ (2006) Sequential quadratic programming. SpringerGoogle Scholar
  28. Ohsaki M (1995) Genetic algorithm for topology optimization of trusses. Comput Struct 57(2):219–225MathSciNetCrossRefzbMATHGoogle Scholar
  29. Ohsaki M, Katoh N (2005) Topology optimization of trusses with stress and local constraints on nodal stability and member intersection. Struct Multidiscip Optim 29(3):190–197MathSciNetCrossRefzbMATHGoogle Scholar
  30. Richardson JN, Adriaenssens S, Bouillard P, Coelho RF (2012) Multiobjective topology optimization of truss structures with kinematic stability repair. Struct Multidiscip Optim 46(4):513–532CrossRefzbMATHGoogle Scholar
  31. Rozvany GI (1996) Difficulties in truss topology optimization with stress, local buckling and system stability constraints. Struct Multidiscip Optim 11(3):213–217MathSciNetCrossRefGoogle Scholar
  32. Sawada K, Matsuo A, Shimizu H (2011) Randomized line search techniques in combined GA for discrete sizing optimization of truss structures. Struct Multidiscip Optim 44(3):337–350CrossRefGoogle Scholar
  33. Stolpe M, Svanberg K (2003) A note on stress-constrained truss topology optimization. Struct Multidiscip Optim 25(1):62–64CrossRefzbMATHGoogle Scholar
  34. Sved G, Ginos Z (1968) Structural optimization under multiple loading. Int J Mech Sci 10(10):803–805CrossRefGoogle Scholar
  35. Tang W, Tong L, Gu Y (2005) Improved genetic algorithm for design optimization of truss structures with sizing, shape and topology variables. Int J Numer Methods Eng 62(13):1737–1762CrossRefzbMATHGoogle Scholar
  36. Xian K, Huang H (2008) Research on algorithm of optimal actuator/sensor location for piezoelectric truss. Chin J Comput Mech 25(6):827–832Google Scholar
  37. Xu B, Ou J, Jiang J (2013) Integrated optimization of structural topology and control for piezoelectric smart plate based on genetic algorithm. Finite Elem Anal Des 64:1–12MathSciNetCrossRefzbMATHGoogle Scholar
  38. Zhou M (1996) Difficulties in truss topology optimization with stress and local buckling constraints. Struct Multidiscip Optim 11(1):134–136CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of AstronauticsBeihang UniversityBeijingChina

Personalised recommendations