A numerical approach to the yield strength of shell structures

Jeremy Bleyer (1, 2) , Patrick de Buhan (2, 1)

1 navier umr 8205 - Laboratoire Navier
2 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes

This work investigates the formulation of lower and upper bound finite elements for the yield design (or limit analysis) of shell structures. The shell geometry is first discretized into triangular planar facets so that previously developed lower bound equilibrium and upper bound kinematic plate finite elements can be coupled to membrane elements. The other main novelty of this paper relies on the formulation of generalized strength criteria for shells in membrane-bending interaction via an implicit upscaling procedure. This formulation provides a natural strategy for constructing lower and upper bound approximations of the exact shell strength criterion and are particularly well suited for a numerical implementation using second-order cone programming tools. By combining these approximate strength criteria to the previously mentioned finite elements, rigorous lower and upper bound ultimate load estimates for shell structures can be computed very efficiently. Different numerical examples illustrate the accuracy as well as the generality and versatility of the proposed approach.

Mots clés: yield design; limit analysis; shells; generalized strength criteria; finite element method; second-order cone programming

Domaines: Matériaux et structures en mécanique [physics.class-ph]

Jeremy Bleyer, Patrick de Buhan. A numerical approach to the yield strength of shell structures. European Journal of Mechanics - A/Solids, 2016, 59, pp.178-194. ⟨10.1016/j.euromechsol.2016.03.002⟩. ⟨hal-01303348⟩