Non-probabilistic reliability-based topology optimization (NRBTO) of continuum structures with displacement constraints via single-loop strategy

In the study, a single-loop strategy is proposed for the non-probabilistic reliability-based topology optimization (NRBTO) of continuum structures with displacement constraints. First, the formulation of topology optimization with displacement constraints is briefly described. Then the interval parametric vertex method is applied to determine the feasible bounds of the displacement responses under unknown-but-bounded uncertainties. To take the effects of interval uncertainties into account, the NRBTO formulation is given. To achieve high efficiency in dealing with the NRBTO problems, the decoupling scheme, i.e., the sequential optimization and reliability assessment method, is applied to decouple the nested process into a single-level procedure. Moreover, a modified performance measure approach (MPMA) is proposed based on the results of a small example to calculate the shift values of displacement constraints. The adjoint vector principle is applied to obtain the sensitivity information between the displacements and the design variables. The results of the two numerical examples indicate that the proposed MPMA can achieve higher efficiency than the traditional performance measure approach.