Analysis and design of reinforced concrete structures as a topology optimization problem

Technical codes for buildings deal with cracked reinforced concrete structures assuming concrete as a compression–only material, whereas rebar provides the structural component with the required tensile strength [1]. Numerical methods can handle reinforced concrete structures calling for demanding non–linear analysis. Indeed, well–known convergence issues arise when copying with concrete as a compression–only material. Recently, an alternative energy–based approach has been proposed to solve the equilibrium of a linear elastic no– tension medium exploiting its hyper–elasticity [2]. A topology optimization problem distributes an equivalent orthotropic material to minimize the strain energy of the no-tension body, thus avoiding more demanding non–linear analysis. This contribution provides an extension to the analysis and optimal design of reinforced concrete structures. Following [3], truss members are modeled within a two–dimensional no–tension continuum in order to model structural elements made of reinforced concrete. The solution of the equilibrium is straightforward within the approach proposed in [2], thus allowing performing analysis at the serviceability limit state with cracked sections. Also, introducing the areas of the reinforcement bars as an additional set of unknowns, a problem of size optimization is outlined to cope with the optimal rebar of r.c. structures. Preliminary numerical simulations are shown to assess the proposed procedure.