Topological gradient in structural optimization under stress and buckling constraints

Florian Mitjana (1) , Sonia Cafieri (2) , Florian Bugarin (3) , Stéphane Segonds (3) , F Castanie (4) , P Duysinx (5)

1 HEC Montréal - HEC Montréal
2 ENAC - Ecole Nationale de l'Aviation Civile
3 ICA - Institut Clément Ader
4 AVANTIS Project
5 Département d’Aérospatiale et de Mécanique [Liège]

Structural topology optimization aims to design mechanical structures by seeking the optimal material layout within a given design space. Within this framework, this paper addresses the minimization of the structural mass under stress and buckling constraints, formulated as a nonlinear combinatorial optimization problem. An algorithm is proposed for such a problem, that follows a topological gradient-based approach. The adjoint method is applied to efficiently compute the constraint gradients. An iterative algorithm for buckling analysis, featuring low memory requirements, is also proposed. Numerical results, including a real application arising in the aeronautical field, illustrate the efficiency of the two proposed algorithms.

Mots clés: topology optimization; topological gradient; buckling constraints

Domaines: Optimisation et contrôle [math.OC]; Recherche opérationnelle [math.OC]; Mécanique des structures [physics.class-ph]

Florian Mitjana, Sonia Cafieri, Florian Bugarin, Stéphane Segonds, F Castanie, et al.. Topological gradient in structural optimization under stress and buckling constraints. Applied Mathematics and Computation, 2021, 409, ⟨10.1016/j.amc.2021.126032⟩. ⟨hal-03134108⟩