Study on stress based topology optimization for reinforced concrete structures

Based on the Drucker-Prager (D-P) criterion for the failure of concrete, a stress based topology optimization method for the design of reinforced concrete structures is studied. Following an extended two-material density penalization scheme, elemental artificial densities are set as the design variables in the optimization problem. The proposed optimization model is constructed as to minimize the steel material volume under concrete Drucker-Prager yield constraints. In order to give a reasonable definition of concrete stress and prevent the stress singularity, the local stress interpolation function and the ε-relaxation technique are employed. With the adjoint-variable sensitivity information of stress constraints, the optimization problem is solved by the gradient-based continuous optimization algorithm. Numerical examples show the validity of the proposed optimization model as well as the efficiency of the numerical techniques. Compared with the conventional compliance minimization method, the obtained optimal solutions are more practicable since they make the best use of the compression strength of concrete and the tensile strength of steel.