An Efficient Strategy for Non-probabilistic Reliability-Based Multi-material Topology Optimization with Evidence Theory

Abstract

It is essential to consider the effects of incomplete measurement, inaccurate information and inadequate cognition on structural topology optimization. For the multi-material structural topology optimization with non-probability uncertainty, the multi-material interpolation model is represented by the ordered rational approximation of material properties (ordered RAMP). Combined with structural compliance minimization, the multi-material topology optimization with reliability constraints is established. The corresponding non-probability uncertainties are described by the evidence theory, and the uniformity processing method is introduced to convert the evidence variables into random variables. The first-order reliability method is employed to search the most probable point under the reliability index constraint, and then the random variables are equivalent to the deterministic variables according to the geometric meaning of the reliability index and sensitivity information. Therefore, the non-probabilistic reliability-based multi-material topology optimization is transformed into the conventional deterministic optimization format, followed by the ordered RAMP method to solve the optimization problem. Finally, through numerical examples of 2D and 3D structures, the feasibility and effectiveness of the proposed method are verified to consider the geometrical dimensions and external loading uncertainties.