Isogeometric analysis for CSG models

Abstract

The IGA (Isogeometric Analysis) was developed as a bridge between CAD and CAE with its highly precise geometry representation. However, IGA can only do little with the models that CAD systems generated in CSG (Constructive Solid Geometry) manner, because the trimmed domain exists. This paper presents a method named Constructive Solid Isogeometric Analysis (CSIGA) to work for CSG models that are composed of primitive solids with union, subtraction and intersection operators. First, this work decomposes the CSG models into several primitive solids represented by NURBS separately, then cuts the primitives with their adjacent ones to produce a set of trimmed tri-variable NURBS primitives, and finally uses Boolean operators to compose them. As to the single trimmed solid, an integration scheme is presented. Meanwhile, a combination scheme has been developed to deal with the union of multiple trimmed solids by using a mortar method. The formulation is verified by applying the isogeometric analysis on several solids which have theoretical solutions such as elliptic cylinder and combined brick, and some tests on multiple trimmed solids are done, too. It is shown that the CSIGA method can deal with CSG models efficiently.