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Numerical upper bounds to the ultimate load bearing capacity of three‐dimensional reinforced concrete structures
Author(s) -
Vincent H.,
Arquier M.,
Bleyer J.,
Buhan P.
Publication year - 2020
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.3144
Subject(s) - homogenization (climate) , limit analysis , finite element method , upper and lower bounds , structural engineering , limit state design , semidefinite programming , degree rankine , mathematics , mathematical optimization , computer science , engineering , mathematical analysis , biodiversity , ecology , process engineering , biology
This contribution is addressing the ultimate limit state design of massive three‐dimensional reinforced concrete structures based on a finite‐element implementation of yield design theory. The strength properties of plain concrete are modeled either by means of a tension cutoff Mohr Coulomb or a Rankine condition, while the contribution of the reinforcing bars is taken into account by means of a homogenization method. This homogenization method can either represent regions of uniformly distributed steel rebars smeared into the concrete domain, but it can also be extended to model single rebars diluted into a larger region, thereby simplifying mesh generation and mesh size requirements in this region. The present paper is mainly focused on the implementation of the upper bound kinematic approach formulated as a convex minimization problem. The retained strength condition for the plain concrete and homogenized reinforced regions are both amenable to a formulation involving positive semidefinite constraints. The resulting semidefinite programming problems can, therefore, be solved using state‐of‐the‐art dedicated solvers. The whole computational procedure is applied to some illustrative examples, where the implementation of both static and kinematic methods produces a relatively accurate bracketing of the exact failure load for this kind of structures.