  While shape optimization using isogeometric shells exhibits appealing
features by integrating design geometries and analysis models, challenges arise
when addressing computer-aided design (CAD) geometries comprised of multiple
non-uniform rational B-splines (NURBS) patches, which are common in practice.
The intractability stems from surface intersections within these CAD models. In
this paper, we develop an approach for shape optimization of non-matching
isogeometric shells incorporating intersection movement. Separately
parametrized NURBS surfaces are modeled using Kirchhoff--Love shell theory and
coupled using a penalty-based formulation. The optimization scheme allows shell
patches to move without preserving relative location with other members during
the shape optimization. This flexibility is achieved through an implicit state
function, and analytical sensitivities are derived for the relative movement of
shell patches. The introduction of differentiable intersections expands the
design space and overcomes challenges associated with large mesh distortion,
particularly when optimal shapes involve significant movement of patch
intersections in physical space. Throughout optimization iterations, all
members within the shell structures maintain the NURBS geometry representation,
enabling efficient integration of analysis and design models. The optimization
approach leverages the multilevel design concept by selecting a refined model
for accurate analysis from a coarse design model while maintaining the same
geometry. We adopt several example problems to verify the effectiveness of the
proposed scheme and demonstrate its applicability to the optimization of the
internal stiffeners of an aircraft wing.
