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

摘要

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