Topology optimization of continuum structures with Drucker–Prager yield stress constraints

This paper presents an efficient topology optimization strategy for seeking the optimal layout of continuum structures exhibiting asymmetrical strength behaviors in compression and tension. Based on the Drucker–Prager yield criterion and the power-law interpolation scheme for the material property, the optimization problem is formulated as to minimize the material volume under local stress constraints. The ε-relaxation of stress constraints is adopted to circumvent the stress singularity problem. For improving the computational efficiency, a grouped aggregation approach based on the Kreisselmeier–Steinhauser function is employed to reduce the number of constraints without much sacrificing the approximation accuracy of the stress constraints. In conjunction with the adjoint-variable sensitivity analysis, the minimization problem is solved by a gradient-based optimization algorithm. Numerical examples demonstrate the validity of the present optimization model as well as the efficiency of the proposed numerical techniques. Moreover, it is also revealed that the optimal design of a structure with pressure-dependent material may exhibit a considerable different topology from the one obtained with pressure-independent material model.