Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method

Enforcing essential boundary conditions plays a central role in immersed boundary methods. Nitsche's idea has proven to be a reliable concept to satisfy weakly boundary and interface constraints. We formulate an extension of Nitsche's method for elasticity problems in the framework of higher order and higher continuity approximation schemes such as the B-spline and non-uniform rational basis spline version of the finite cell method or isogeometric analysis on trimmed geometries. Furthermore, we illustrate a significant improvement of the flexibility and applicability of this extension in the modeling process of complex 3D geometries. With several benchmark problems, we demonstrate the overall good convergence behavior of the proposed method and its good accuracy. We provide extensive studies on the stability of the method, its influence parameters and numerical properties, and a rearrangement of the numerical integration concept that in many cases reduces the numerical effort by a factor two. A newly composed boundary integration concept further enhances the modeling process and allows a flexible, discretization-independent introduction of boundary conditions. Finally, we present our strategy in the framework of the modeling and isogeometric analysis process of trimmed non-uniform rational basis spline geometries.