Revisiting topology optimization with buckling constraints

  • Federico FerrariEmail author
  • Ole Sigmund
Research Paper


We review some features of topology optimization with a lower bound on the critical load factor, as computed by linearized buckling analysis. The change of the optimized design, the competition between stiffness and stability requirements and the activation of several buckling modes, depending on the value of such lower bound, are studied. We also discuss some specific issues which are of particular interest for this problem, as the use of non-conforming finite elements for the analysis, the use of inconsistent sensitivity that may lead to wrong signs of sensitivities and the replacement of the single eigenvalue constraints with an aggregated measure. We discuss the influence of these practices on the optimization result, giving some recommendations.


Topology optimization Eigenvalue optimization Linearized buckling Aggregation functions Finite elements Sensitivity analysis 



The current project is supported by the Villum Fonden through the Villum Investigator Project “InnoTop.” The authors are grateful to Prof. Pauli Pedersen for several fruitful discussions on the topic of the paper.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkKongens LyngbyDenmark

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