Non-probabilistic reliability-based topology optimization of continuum structures considering local stiffness and strength failure

Abstract

This study presents a novel non-probabilistic reliability-based topology optimization (NRBTO) framework to determine optimal material configurations for continuum structures under local stiffness and strength limits. Uncertainty quantification (UQ) analysis under unknown-but-bounded (UBB) inputs is conducted to determine the feasible bounds of structural responses by combining a material interpolation model with stress aggregation function and interval mathematics. For safety reasons, improved interval reliability indexes that correspond to displacement and stress constraints are applied in topological optimization issues. Meanwhile, an adjoint-vector based sensitivity analysis is further discussed from which the gradient features between reliability measures and design variables are mathematically deduced, and the computational difficulties in large-scale variable updating can be effectively overcome. Numerical examples are eventually given to demonstrate the validity of the developed NRBTO methodology.