Non-probabilistic reliability-based topology optimization of continuum structures

It is of great importance to incorporate uncertainties into structural topology optimization problems. Based on the definition of the non-probabilistic reliability index, this paper proposes a mathematical model for topology optimization of 3D continuum structures with non-probabilistic reliability constraints on deformation. In this model, the uncertainties in material properties, geometrical dimensions and loading conditions are accounted for. The Performance Measure Approach (PMA) is adopted for transformation of the constraints. In this context, the adjoint variable scheme for sensitivity analysis of the target performance is discussed, which facilitates a mathematical programming solution of the optimization problem. Numerical investigations illustrate the applicability and the validity of the present model as well as the proposed numerical techniques. The computational results show that non-probabilistic reliability-based topology optimization may yield more reasonable material layouts than the conventional deterministic approach.