Uncertainty-oriented topology optimization of interval parametric structures with local stress and displacement reliability constraints

Abstract

This paper presents the interval reliability-based topology optimization (IRBTO) framework and an effective solution procedure for interval parametric structures to achieve optimal material configurations under consideration of local stiffness and strength failure. Firstly, ε-relaxed stress criterion and global stress aggregation approach are involved to circumvent the stress singularity and multi-constrained problems. Combined the orthogonal polynomial expansion with the set allocation theorem, an interval dimension-by-dimension method (IDDM) is proposed to determine feasible bounds of structural responses under unknown-but-bounded load and material uncertainties. The interval reliability (IR) is then applied to handle the limited reliability constraints of concerned displacements and the global stress measure. Meanwhile, the adjoint-vector based sensitivity analysis of presented IR indexes to design variables is further discussed to avoid expensive computational cost from the large-scale nature of variable updating. The usage, rationality, and superiority of the developed methodology are demonstrated by several case applications.