  We introduce the isogeometric shape optimisation of thin shell structures
using subdivision surfaces. Both triangular Loop and quadrilateral
Catmull-Clark subdivision schemes are considered for geometry modelling and
finite element analysis. A gradient-based shape optimisation technique is
implemented to minimise compliance, i.e. to maximise stiffness. Different
control meshes describing the same surface are used for geometry
representation, optimisation and finite element analysis. The finite element
analysis is performed with subdivision basis functions corresponding to a
sufficiently refined control mesh. During iterative shape optimisation the
geometry is updated starting from the coarsest control mesh and proceeding to
increasingly finer control meshes. This multiresolution approach provides a
means for regularising the optimisation problem and prevents the appearance of
sub-optimal jagged geometries with fine-scale oscillations. The finest control
mesh for optimisation is chosen in accordance with the desired smallest feature
size in the optimised geometry. The proposed approach is applied to three
optimisation examples, namely a catenary, a roof over a rectangular domain and
a freeform architectural shell roof. The influence of the geometry description
and the used subdivision scheme on the obtained optimised curved geometries is
investigated in detail.
