Summary: Lattice-skin structures composed of a thin-shell skin and a lattice infill are widespread in nature and large-scale engineering due to their efficiency and exceptional mechanical properties. Recent advances in additive manufacturing, or 3D printing, make it possible to create lattice-skin structures of almost any size with arbitrary shape and geometric complexity. We propose a novel gradient-based approach to optimizing both the shape and infill of lattice-skin structures to improve their efficiency further. The respective gradients are computed by fully considering the lattice-skin coupling while the lattice topology and shape optimization problems are solved in a sequential manner. The shell is modeled as a Kirchhoff-Love shell and analyzed using isogeometric subdivision surfaces, whereas the lattice is modeled as a pin-jointed truss. The lattice consists of many cells, possibly of different sizes, with each containing a small number of struts. We propose a penalization approach akin to the SIMP (solid isotropic material with penalization) method for topology optimization of the lattice. Furthermore, a corresponding sensitivity filter and a lattice extraction technique are introduced to ensure the stability of the optimization process and to eliminate scattered struts of small cross-sectional areas. The developed topology optimization technique is suitable for nonperiodic, nonuniform lattices. For shape optimization of both the shell and the lattice, the geometry of the lattice-skin structure is parameterized using the free-form deformation technique. The topology and shape optimization problems are solved in an iterative, sequential manner. The effectiveness of the proposed approach and the influence of different algorithmic parameters are demonstrated with several numerical examples.
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