Embedded structural entities in NURBS-based isogeometric analysis

The core idea of this article is nested parametrization in the context of isogeometric analysis. The method has been inspired by trimming procedures and can be applied to different applications like local modifications and enhancements of thin-walled structures or coupling of two overlying elements by embedding one in the other. A remodeling for an explicit representation of the boundaries is avoided, which would be contradictory to the aim of isogeometric analysis of using the original CAD model. The nested entity is directly linked to the super element, however its element formulation is independent of the super element formulation within this article. The derivation, implementation and application is shown in particular for one-dimensional entities embedded into 2D domains. Consequently, the definition of an embedded curve in the surface is required and realized by using NURBS curves in the parameter space of the corresponding surface. This curve with its respective predefined base vectors serves as the basis for new element formulations or adaptation of already developed element formulations, which are based on the geometric description of a curve. In detail, an adapted formulation of the recently developed nonlinear isogeometric spatial Bernoulli Beam by the authors is presented in this paper. Furthermore, those embedded curves are used for line supports and loads, as well as a mass manipulation. The accuracy of the proposed element formulation is verified by several benchmark examples and the potential for future applications is briefly revealed.