Isogeometric analysis with trimmed geometries applied to ship hulls

Abstract

This Paper aims to investigate Trimmed NURBS surfaces for Isogeometric Analysis(IGA). NURBS are Non-Rational B-spline functions which are widely used for geometric modelling in most Computer aided Design programs. This is because they have the ability to represent a wide range of curves, surfaces and solids. When models are created in CAD and imported in to Finite Element programs for analysis, the geometry is approximated, and the resulting model is less accurate. IGA aims to close the gap between design and analysis by performing analysis directly on the geometry from CAD. IGA therefore also use NURBS in analysis. A walk-through of the theory behind NURBS curves and surfaces are presented in this paper. \\ One problem with IGA is that trimming is a very common practice when constructing complex geometries in CAD. Trimming does not actually change the mathematical description of the surface, it simply renders the trimmed part invisible. This means that when analysis is performed on a trimmed surface, the surface will behave exactly like the surface before the trimming. The main purpose of this thesis is to investigate how to perform analysis on trimmed NURBS surfaces.