A conformal optimization framework for lightweight design of complex components using stochastic lattice structures

Multi-scale lattice structures are celebrated for their superior mechanical properties and have been widely adopted across various engineering disciplines. Traditional periodic multi-scale lattice structures, however, often struggle with maintaining the fidelity of the original model's boundaries, encounter complex geometric modeling processes, and require extensive optimization times. This paper introduces a conformal optimization design framework for three-dimensional lattice structures that can be efficiently and conveniently applied to design domains with complex or irregular boundaries. The framework capitalizes on the unique properties of Stochastic Lattice Structures (SLS), which provide greater design flexibility and reduced sensitivity to defects compared to periodic counterparts. We present the Three-dimensional Functionally Graded Stochastic Lattice Structures (3D-FGSLS) design framework, which includes four main components: a database for optimization and geometric modeling that links microstructure's relative density with its geometric parameters and mechanical properties; a homogenization-based optimization design method; a novel vertex-based density mapping approach; and a advanced software kernel for lattice geometric modeling. The effectiveness of this framework is validated through several cases, showcasing its practical applicability.