Surface lattice structure design via computational conformal mapping and structural optimization

This paper presents a novel approach for optimizing graded lattice structures embedded in curved shell surfaces, combining computational conformal mapping (CCM) with structural optimization. Using the moving morphable components framework, we define the topological configuration of lattice structures with few geometry-related design variables, which reduces computational complexity. Partitioned coordinate mapping, constructed with the B-spline basis functions, enables the non-uniform lattice structures generation with smooth transitions between neighboring unit cells. Furthermore, CCM-based mesh parameterization maps general triangulated surfaces to a planar domain with low distortion, on which we define the MMC-based topology description function (TDF) for the graded lattice with closed-form, adjoint-consistent derivatives and seam-safe continuity. This integrated approach simultaneously optimizes the shape and size of lattice structures on curved surfaces, preserving structural boundary clarity without filtering operators while balancing aesthetic appearance with structural performance. The proposed method provides an efficient pathway for the optimization of complex graded lattice structures embedded in curved surfaces.