Reliability-based topology optimization for heterogeneous composite structures under interval and convex mixed uncertainties

With the rapid development of intelligent manufacturing and smart design, the optimal design conception for composite laminates is arising more attentions in both academic and engineering fields. Note that most of the current researches focus on the deterministic laminate design whereas the uncertainty-oriented topological design scheme for heterogeneous composites are rarely considered. In view of this, this study will present a new layout optimization process which combines the hybrid uncertainty quantification analysis and non-probabilistic reliability-based topology optimization (NRBTO). Owing to the sample limitation of multi-source uncertainties in material properties and external loads, the non-statistical convex-theoretical set theory is first explored to determine displacement response bounds of multi-layer structures under anisotropic constitutive relationship. As the safety judgment, a novel reliability index corresponding to the local stiffness features is defined via interval and convex mixed uncertainties, and its explicit expression is further deduced by the set-interference principle. To ensure the robustness and convergence of the large-scale iteration in NRBTO framework, the adjoint equations are also analyzed for the design sensitivity updating and the gradient algorithm is involved as well. Several typical optimization cases are presented to demonstrate the validity and effectiveness of the developed methodology.