An Efficient Sequential Strategy for Non-probabilistic Reliability-based Topology Optimization (NRBTO) of Continuum Structures with Stress Constraints

Abstract

In the study, the sequential strategy is proposed for non-probabilistic reliability-based topology optimization (NRBTO) of continuum structures with stress constraints. Firstly, the qp-relaxation criterion is involved to circumvent the stress singularity. Then the deterministic topology optimization formulation by Stress-Influence-Function (SIF) approach is described. Uncertainty quantification analysis is conducted to determine the feasible bounds of the elemental stresses under unknown-but-bounded uncertainties. For safety reasons, the non-probabilistic reliability concept is introduced in the optimization formulation. The sequential strategy is proposed to handle the NRBTO problem and thus the original nested process of topology optimization and reliability analysis was decoupled, in which the update of design variables and the shift of the strength feature in the stress influence function are conducted alternately in the optimization process. The Performance Measure Approach (PMA) is applied to calculate the shift value of the strength feature and a shift value function is presented to avoid the numerical oscillations caused by the large variation of strength feature. Three numerical examples are eventually given to illustrate the applicability and validity of the developed sequential strategy for NRBTO with stress constraints.