  This work focuses on the coupling of trimmed shell patches using Isogeometric
Analysis, based on higher continuity splines that seamlessly meet the $C^1$
requirement of Kirchhoff-Love-based discretizations. Weak enforcement of
coupling conditions is achieved through the symmetric interior penalty method,
where the fluxes are computed using their correct variationally consistent
expression that was only recently proposed and is unprecedentedly adopted
herein in the context of coupling conditions. The constitutive relationships
account for generically laminated materials, although the proposed tests are
conducted under the assumption of uniform thickness and lamination sequence.
Numerical experiments assess the method for an isotropic and a laminated plate,
as well as an isotropic hyperbolic paraboloid shell from the new shell obstacle
course. The boundary conditions and domain force are chosen to reproduce
manufactured analytical solutions, which are taken as reference to compute
rigorous convergence curves in the $L^2$, $H^1$, and $H^2$ norms, that closely
approach optimal ones predicted by theory. Additionally, we conduct a final
test on a complex structure comprising five intersecting laminated cylindrical
shells, whose geometry is directly imported from a STEP file. The results
exhibit excellent agreement with those obtained through commercial software,
showcasing the method's potential for real-world industrial applications.
