Multiscale reliability-based topology optimization methodology for truss-like microstructures with unknown-but-bounded uncertainties

This paper introduces a new optimization framework to multiscale structures with unknown-but-bounded (UBB) uncertainties, where the optimal design is applied at two scales: the macroscale, i.e., the structural level, where the non-probabilistic reliability-based topology optimization (NRBTO) is conducted, and the microscale, i.e., the material level, where the non-probabilistic reliability-based design optimization (NRBDO) for truss-like cell dimensions is achieved. By combination of the homogenization method and interval mathematics, rules of macro-micro stiffness equivalence as well as interval bounds of macro displacement responses under specific micro structural settings can be first confirmed. For safety reasons, novel reliability definitions are respectively given for the double-level design, in which the offset factor with good differential properties is applied for the NRBTO and the matching factor derived from the improved rule of interval sorting is utilized for the NRBDO. To circumvent problems of large-scale variable updating in two-level optimization procedures, the adjoint-based vector in macro layout design as well as the particle swarm optimization (PSO) algorithm in micro parametric design are further discussed. The usage, effectiveness, and the superiority of the developed methodology are eventually demonstrated by two 3D engineering applications.