Graded infill design of thin-walled structures with connectable nonuniform microstructures based on the data-driven surrogate model

This paper proposes a structural optimization framework for the high-performance and lightweight design of curved thin-shell structures. The proposed method integrates conformal mapping, a parameterized level-set method (PLSM), and a Kriging-based surrogate modeling strategy to obtain the graded infill design of thin-walled structures. At the macroscopic level, conformal mapping is employed to project the original three-dimensional (3D) curved surface onto a two-dimensional (2D) parametric domain, thereby reducing the dimension of the design problem. At the microscopic level, PLSM is introduced to define multiple prototype microstructures with diverse geometric features. A shape interpolation method is then developed to map these prototypes into a family of nonuniform microstructures. To reduce the computational burden, these microstructures serve as sample points to construct a Kriging metamodel for efficient property prediction. Through a mapping-design-inverse mapping process, the optimized graded microstructures are precisely projected back onto the original 3D surface while preserving geometric fidelity. The objective function is to minimize structural compliance subject to a global volume constraint. Sensitivity analysis formulas are derived based on a conformal thin-shell finite element model and PLSM, and expansion coefficients of the prototype microstructures are updated using the Optimality Criteria (OC) method. The effectiveness of the proposed framework is demonstrated through two examples: a vase shell and a turbine blade shell.