Stress-based topology optimization of concrete structures with prestressing reinforcements

Following the extended two-material density penalization scheme, a stress-based topology optimization method for the layout design of prestressed concrete structures is proposed. The Drucker-Prager yield criterion is used to predict the asymmetrical strength failure of concrete. The prestress is considered by making a reasonable assumption on the prestressing orientation in each element and adding an additional load vector to the structural equilibrium function. The proposed optimization model is thus formulated as to minimize the reinforcement material volume under Drucker-Prager yield constraints on elemental concrete local stresses. In order to give a reasonable definition of concrete local stress and prevent the stress singularity phenomenon, the local stress interpolation function and the ε -relaxation technique are adopted. The topology optimization problem is solved using the method of moving asymptotes combined with an active set strategy. Numerical examples are given to show the efficiency of the proposed optimization method in the layout design of prestressed concrete structures.