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

• Published in: Computers & structures Vol. 296; p. 107295
• Main Authors: Canelas, Alfredo, Carrasco, Miguel, López, Julio
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2024
• Subjects: Bernstein approximation; Conic programming; Reliability design optimization; Robust optimization; Topology optimization; Topology optimization; Robust optimization; Reliability design optimization; Conic programming; Bernstein approximation
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2024.107295

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. •A topology optimization model for design of robust trusses is proposed.•A failure probability constraint in the compliance of the truss is considered.•The failure probability is approximated using the Bernstein inequality.•A tractable convex conic reformulation of the optimization model is obtained.•Numerical examples show that the conic reformulation enables time-saving.