Yield Design of Periodically Heterogeneous Plates

Jérémy Bleyer (1) , Duc Toan Pham (1, 2) , Patrick de Buhan (1) , Céline Florence (2)

1 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
2 CSTB - Centre Scientifique et Technique du Bâtiment

This work addresses the determination of the overall strength capacities of periodically heterogeneous plates within a yield design framework. Illustrative applications focus, notably, on reinforced concrete slabs in fire conditions. A homogenization procedure and related numerical tools are proposed to compute macroscopic strength criteria expressed in terms of generalized forces (membrane and bending solicitations). To this end, a yield design auxiliary problem is formulated on the representative three-dimensional unit cell and a numerical resolution by a static approach is presented, making use of simple 3D equilibrium finite elements. A particular emphasis is put on the link between the local strength criterion of steel and concrete and the resulting optimization problem, which can be formulated, either as a second-order cone programming (SOCP) problem or, more generally, as a semi-definite programming (SDP) problem. A first illustrative example of a concrete slab with a single array of steel bars will be used to validate the approach. Then, the influence of fire conditions on the strength capacities of reinforced concrete slabs will be investigated and numerical computations will be confronted to experimental results.

Keywords: periodic plates; conic programming; fire conditions; finite elements; yield design; limit analysis

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

Jérémy Bleyer, Duc Toan Pham, Patrick de Buhan, Céline Florence. Yield Design of Periodically Heterogeneous Plates. Springer International Publishing. Direct Methods for Limit and Shakedown Analysis of Structures, 220, Springer International Publishing, pp.143-158, 2015, Advanced Computational Algorithms and Material Modelling Series: Solid Mechanics and Its Applications, 978-3-319-12928-0. ⟨10.1007/978-3-319-12928-0_8⟩. ⟨hal-01115853⟩