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

Abstract

This paper introduces a 3D equilibrium-based finite element formulation for reinforced concrete. The stress unknowns in the proposed formulation strongly satisfy the equilibrium equations throughout the entire volume, with the exception of the mesh interfaces where the rebars intersect. The concrete stress tensor is interpolated using tetrahedral piece-wise linear elements 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 an in–house interior point algorithm.