Modeling of geometric uncertainties in topology optimization via the shift of design nodes

Abstract

In the practical environment, the mechanical structures suffer from the geometric uncertainties which vary either spatially and directionally, and the performance may be degraded in consequence. For a reliable design under those uncertainties, this paper introduces a reliability-based topology optimization framework under geometric uncertainty using nodal design variables. In a nodal density-based topology optimization scheme, a structural layout is presented through the density field constructed by a distance-based interpolation of nodal densities. Geometric variation of a structure under uncertainty is modeled via the shift of design nodes, followed by the perturbation of the density field. The direction and magnitude of the nodal shift are determined from the random field discretized by Karhunen-Loeve expansion and a pseudo-gradient function of the density field. A reliability-based topology optimization problem is formulated into a double loop scheme based on the proposed geometric uncertainty model. Then it is decoupled using sequential optimization and reliability assessment method and the sensitivities are derived analytically. The numerical examples under geometric uncertainties, including both spatially and directionally non-uniform uncertainties, are demonstrated to validate the proposed optimization framework.