Isogeometric analysis with strong multipatch C1-coupling

Abstract

C1 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 (Gómez 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 C0. In particular, enforcing C1 continuity on certain domains can result in “C1-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 C1-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 G1 continuity. Numerical studies are conducted for problems involving linear elasticity, Kirchhoff–Love shells and Cahn–Hilliard equation.