hal-01115853
https://enpc.hal.science/hal-01115853
https://enpc.hal.science/hal-01115853/document
https://enpc.hal.science/hal-01115853/file/DM_book_periodic_plates_hal.pdf
doi:10.1007/978-3-319-12928-0_8
[ENPC] Ecole des Ponts ParisTech
[CSTB] Centre Scientifique et Technique du Bâtiment
[CNRS] CNRS - Centre national de la recherche scientifique
[UR-NAVIER] Laboratoire Navier
[PARISTECH] ParisTech
[MULTI-ECHELLE] MULTI-ECHELLE
[IFSTTAR] Ifsttar
[UNIV-EIFFEL] Université Gustave Eiffel
[IFSTTAR-UNIVEIFFEL] Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux
Yield Design of Periodically Heterogeneous Plates
Bleyer, Jérémy
Pham, Duc Toan
de Buhan, Patrick
Florence, Céline
[PHYS.MECA.MSMECA] Physics [physics]/Mechanics [physics]/Materials and structures in mechanics [physics.class-ph]
COUV
periodic plates
conic programming
fire conditions
finite elements
yield design
limit analysis
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.
2015
2015-03-28
en
Direct Methods for Limit and Shakedown Analysis of Structures
Springer International Publishing