Non-parametric data-driven approach to reliability-based topology optimization of trusses under uncertainty of material constitutive law

The material behavior intrinsically possesses the aleatory uncertainty (i.e., the natural variability). Against uncertainty in a given data set of elastic material responses, this paper presents a data-driven approach to reliability-based truss topology optimization under the compliance constraint. We utilize the order statistics to guarantee the confidence level of the probability that the reliability on the compliance constraint is no smaller than the target reliability, and formulate the truss optimization problem in a bi-level optimization form. By using the duality of linear optimization, we recast this bi-level optimization problem as a single-level optimization problem, which can be solved with a standard nonlinear optimization approach. Numerical examples illustrate the validity, as well as the characteristic of optimal solutions, of the proposed method.