  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 optimising 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 optimisation problems are solved in a sequential
manner. The shell is modelled as a Kirchhoff-Love shell and analysed using
isogeometric subdivision surfaces, whereas the lattice is modelled 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 penalisation
approach akin to the SIMP (solid isotropic material with penalisation) method
for topology optimisation of the lattice. Furthermore, a corresponding
sensitivity filter and a lattice extraction technique are introduced to ensure
the stability of the optimisation process and to eliminate scattered struts of
small cross-sectional areas. The developed topology optimisation technique is
suitable for non-periodic, non-uniform lattices. For shape optimisation of both
the shell and the lattice, the geometry of the lattice-skin structure is
parameterised using the free-form deformation technique. The topology and shape
optimisation 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.
