TY - JOUR

T1 - Topology optimization of truss structures under failure probability using the Bernstein approximation

AU - Canelas, Alfredo

AU - Carrasco, Miguel

AU - López, Julio

N1 - Publisher Copyright:
© 2024

PY - 2024/6/1

Y1 - 2024/6/1

N2 - 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.

AB - 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.

KW - Bernstein approximation

KW - Conic programming

KW - Reliability design optimization

KW - Robust optimization

KW - Topology optimization

UR - http://www.scopus.com/inward/record.url?scp=85183456258&partnerID=8YFLogxK

U2 - 10.1016/j.compstruc.2024.107295

DO - 10.1016/j.compstruc.2024.107295

M3 - Article

AN - SCOPUS:85183456258

SN - 0045-7949

VL - 296

SP - 1

EP - 10

JO - Computers and Structures

JF - Computers and Structures

M1 - 107295

ER -