TOPOLOGY OPTIMIZATION OF LOAD BEARING CAPACITY FOR STRUCTURES WITH DIFFERENT TENSILE/COMPRESSIVE STRENGTHS

Leyla Mourad (1) , Jeremy Bleyer (1) , Romain Mesnil (1) , Joanna Nseir , Wassim Raphael , Karam Sab (1)

1 NAVIER UMR 8205 - Laboratoire Navier

This work extends the theory of limit analysis [2, 5] which consists in computing a structure maximum load bearing capacity to topology optimization problems. Here we aim at finding a structure which maximizes the load-bearing capacity, given some material strength properties, on a fixed computational domain with a given material volume constraint. The problem is relaxed to a convex optimization problem by considering a continuous fictitious density field. We show that this problem is equivalent to minimizing the total volume such that the structure can withstand a given fixed loading [3, 1]. State-ofthe-art conic programming solvers [4] are used for computing the solutions to the convex optimization problems. Finally a SIMP-like penalty method is proposed to obtain discrete topologies. Materials with asymmetric tensile and compressive strengths are considered, with the particular case of no-tension materials. Examples illustrating the efficiency of the proposed method will finally be presented.

Keywords: Topology optimization; Limit analysis; Convex optimization

Domains: Materials and structures in mechanics [physics.class-ph]

Leyla Mourad, Jeremy Bleyer, Romain Mesnil, Joanna Nseir, Wassim Raphael, et al.. TOPOLOGY OPTIMIZATION OF LOAD BEARING CAPACITY FOR STRUCTURES WITH DIFFERENT TENSILE/COMPRESSIVE STRENGTHS. 14th World Congress on Computational Mechanics (WCCM), Jan 2021, Paris (virtual), France. ⟨hal-03148136⟩