Shells, as part of thin-walled structures, are well-known and used in many engineering applications thanks to their efficient load-carrying behavior and lightweightness. In recent years, Isogeometric Analysis (IGA) has emerged as a powerful approach for modeling and simulating these slender, curved structures. By employing Non-Uniform Rational B-Splines (NURBS) as shape functions in finite element analysis, IGA offers superior accuracy and the potential of seamless integration with CAD models [1,2]. Furthermore, its extension towards CAD-based B-Rep representation (IBRA) [3] opens the possibility to more complex applications with a trimmed multipatch model. This contribution investigates the coupling methods on trimmed multipatch Kirchhoff-Love and Reissner-Mindlin shell structures by employing weak imposition techniques such as the penalty and Nitsche-type methods [4]. Two open questions are addressed: first, how the trimmed multipatch interface impacts the accuracy and stability of the Nitsche-type method, and second, how the Nitsche-type method's performance is affected by small-cut elements, where singularities lead to infinite traction forces in shell cases. To address the latter issue, switching to the penalty method may enhance simulation robustness. Several widely recognized shell benchmarks are utilized to validate the findings. REFERENCES [1] Kiendl, J., Bletzinger, K. U., Linhard, J., & Wüchner, R. (2009). Isogeometric shell analysis with Kirchhoff–Love elements. Computer methods in applied mechanics and engineering, 198(49-52), 3902-3914. [2] Benson, D. J., Bazilevs, Y., Hsu, M. C., & Hughes, T. (2010). Isogeometric shell analysis: the Reissner–Mindlin shell. Computer Meth-ods in Applied Mechanics and Engineering, 199(5-8), 276-289. [3] Breitenberger, M., Apostolatos, A., Philipp, B., Wüchner, R., & Bletzinger, K. U. (2015). Analysis in computer aided design: Nonlinear isogeometric B-Rep analysis of shell structures. Computer Methods in Applied Mechanics and Engineering, 284, 401-457. [4] Apostolatos, A., Bletzinger, K. U., & Wüchner, R. (2019). Weak imposition of constraints for structural membranes in transient geometrically nonlinear isogeometric analysis on multipatch surfaces. Computer Methods in Applied Mechanics and Engineering, 350, 938-994.