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.