Layout design of reinforced concrete structures using two-material topology optimization with Drucker–Prager yield constraints

This paper aims to develop a method that can automatically generate the optimal layout of reinforced concrete structures by incorporating concrete strength constraints into the two-material topology optimization formulation. The Drucker–Prager yield criterion is applied to predict the failure behavior of concrete. By using the power-law interpolation, the proposed optimization model is stated as a minimum compliance problem under the yield stress constraints on concrete elements and the material volume constraint of steel. The ε-relaxation technique is employed to prevent the stress singularity. A hybrid constraint-reduction strategy, in conjunction with the adjoint-variable sensitivity information, is integrated into a gradient-based optimization algorithm to overcome the numerical difficulties that arise from large-scale constraints. It can be concluded from numerical investigations that the proposed model is suitable for obtaining a reasonable layout which makes the best uses of the compressive strength of concrete and the tensile strength of steel. Numerical results also reveal that the hybrid constraint-reduction strategy is effective in solving the topology optimization problems involving a large number of constraints.