CAD Aspects on Isogeometric Analysis and Hybrid Domains

This thesis is the result of a Ph.D. program in Alto Apprendistato carried out at the Dipartimento di Informatica - Scienza e Ingegneria (DISI) of the University of Bologna and at the company devDept Software. With regard to the professional side of my Individual Training Project, I developed technical and scientific skills in 3D geometry of curves and surfaces, CAD, and Finite Element Analysis (FEA). Regarding the academic side, I investigated CAD aspects in the field of Isogeometric Analysis (IGA) on both single and hybrid multipatch physical domains. Simulations are performed in classical FEA systems, which require the conversion of designs, made by CAD systems, into finite element meshes. IGA is a new approach that aims to unify the worlds of CAD and FEA by using the same geometry for analysis as what is used for modeling. That is, the same set of basis functions are adopted both to describe the computational geometry in the CAD tool, and to span the solution space for FEA. The traditional FEA pipeline works on meshes and the most advanced IGA systems work on NURBS or T-spline geometries. Hybrid geometric models (i.e., models in which mesh and NURBS entities coexist), are an emergent way to represent a solid object, but in most CAD systems mesh and NURBS geometries cannot interact with each other, and conversions to a common representation are often needed. In this thesis, we investigate how IGA can be applied on 2D and 3D hybrid models made by both mesh and NURBS entities without requiring laborious and time consuming conversion processes.