Isogeometric continuity constraints for multi-patch shells governed by fourth-order deformation and phase field models

This work presents numerical techniques to enforce continuity constraints on multi-patch surfaces for three distinct problem classes. The first involves structural analysis of thin shells that are described by general Kirchhoff-Love kinematics. Their governing equation is a vector-valued, fourth-order, nonlinear, partial differential equation (PDE) that requires at least C^1continuity within a displacement-based finite element formulation....