Isogeometric analysis with strong multipatch C1-coupling

Abstract C 1 continuity is desirable for solving 4th order partial differential equations such as those appearing in Kirchhoff–Love shell models ( Kiendl et al., 2009 ) or Cahn–Hilliard phase field applications ( Gomez et al., 2008 ). Isogeometric analysis provides a useful approach to obtaining approximations with high-smoothness. However, when working with complex geometric domains composed of multiple patches, it is a challenging task to achieve global continuity beyond C 0 . In particular, enforcing C 1 continuity on certain domains can result in “ C 1 -locking” due to the extra constraints applied to the approximation space ( Collin et al., 2016 ). In this contribution, a general framework for coupling surfaces in space is presented as well as an approach to overcome C 1 -locking by local degree elevation along the patch interfaces. This allows the modeling of solutions to 4th order PDEs on complex geometric surfaces, provided that the given patches have G 1 continuity. Numerical studies are conducted for problems involving linear elasticity, Kirchhoff–Love shells and Cahn–Hilliard equation.

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