Topology optimization of truss structures under failure probability using the Bernstein approximation

Alfredo Canelas*, Miguel Carrasco*, Julio López*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A novel topology optimization approach for the robust design of structures is presented. The method considers both deterministic and random loadings, and minimizes the compliance subject to a constraint on the volume, as well as a constraint on the failure probability. Handling the failure probability is often challenging in numerical terms, potentially leading to an intractable model as the problem scales. It is addressed by employing the Bernstein approximation, resulting in a model that has the remarkable property of being a linear conic programming problem, therefore, solvable in polynomial time with respect to the input size by using interior point methods. Furthermore, a more efficient reformulation of the problem, involving small semidefinite constraints is derived. To demonstrate the practicality of the proposed method, solutions to several examples of truss topology optimization are provided.

Original languageEnglish
Article number107295
Pages (from-to)1-10
Number of pages10
JournalComputers and Structures
StatePublished - 1 Jun 2024

Bibliographical note

Publisher Copyright:
© 2024


  • Bernstein approximation
  • Conic programming
  • Reliability design optimization
  • Robust optimization
  • Topology optimization


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