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Article Dans Une Revue Computers & Structures Année : 2023

Elastoplastic and limit analysis of reinforced concrete with an equilibrium-based finite element formulation

Résumé

In this paper, a 3D equilibrium-based finite element formulation is presented for reinforced concrete, where the stress unknowns strongly satisfy the equilibrium equations. The concrete stress tensor is interpolated using tetrahedral piece-wise linear element with statically admissible discontinuities, while the rebars are considered as 1D elements embedded into the concrete, intersecting the triangular mesh. Thus, the global equilibrium is ensured by writing for each face of the mesh the traction continuity equation, while including the rebar stress contribution for the intersected triangular faces. The elastic equilibrium formulation is then written into an equivalent optimization problem, extended to the elastoplastic case by simply adding semi-definite matrix constraints on the concrete stress tensor, corresponding to a Rankine or a truncated Mohr-Coulomb criterion. As for the rebars, they are considered to obey a 1D perfectly elastoplastic behavior. The present formulation is also developed for limit analysis, to directly obtain an estimate of the lower bound of the collapse load. The resulting semi-definite programming optimization problems are solved using a in-house interior point algorithm.
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Dates et versions

hal-04157914 , version 1 (10-07-2023)

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Mohammed-Khalil Ferradi, Agnès Fliscounakis, Mathieu Arquier, Jeremy Bleyer. Elastoplastic and limit analysis of reinforced concrete with an equilibrium-based finite element formulation. Computers & Structures, 2023, 286, pp.107095. ⟨10.1016/j.compstruc.2023.107095⟩. ⟨hal-04157914⟩
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