Isogeometric analysis with strong multipatch C~1-coupling

摘要

C1continuity is desirable for solving 4th order partial differential equations such as those appearing in Kirchhoff–Love shell models () or Cahn–Hilliard phase field applications (). 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 beyondC0. In particular, enforcingC1continuity on certain domains can result in “C1-locking” due to the extra constraints applied to the approximation space ().In this contribution, a general framework for coupling surfaces in space is presented as well as an approach to overcomeC1-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 haveG1continuity. Numerical studies are conducted for problems involving linear elasticity, Kirchhoff–Love shells and Cahn–Hilliard equation.