Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1213–1232 | Cite as

Including global stability in truss layout optimization for the conceptual design of large-scale applications

  • Alexis Tugilimana
  • Rajan Filomeno Coelho
  • Ashley P. Thrall


Including stability in truss topology optimization is critical to avoid unstable optimized designs in practical applications. While prior research addresses this challenge by implementing local buckling and linear prebuckling, numerical difficulties remain due to the global stability singularity phenomenon. Therefore, the goal of this paper is to develop an optimization formulation for truss topology optimization including global stability without numerical singularities, within the framework of the preliminary design of large-scale structures. This task is performed by considering an appropriate simultaneous analysis and design formulation, in which the use of a disaggregated form for the equilibrium equations alleviates the singularities inherent to global stability. By implementing a local buckling criterion for hollow truss elements, the resulting formulation is well-suited for the preliminary design of large-scale trusses in civil engineering applications. Three applications illustrate the efficiency of the proposed approach, including a benchmark truss structure and the preliminary design of a footbridge and a dome. The results demonstrate that including local buckling and global stability can considerably affect the optimized design, while offering a systematic means of avoiding unstable solutions. It is also shown that the proposed approach is in a good agreement with linear prebuckling assumptions.


Truss topology optimization Local buckling Global stability Nonlinear semidefinite programming Simultaneous analysis and design 



The authors would like to thank the Fond National de la Recherche Scientifique (F.R.S-FNRS, Belgium) for its financial support.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.BATir DepartmentUniversité libre de BruxellesBrusselsBelgium
  2. 2.Department of Civil & Environmental, Earth SciencesUniversity of Notre DameNotre DameUSA

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