Isogeometric Analysis: Toward Unification of Computer Aided Design and Finite Element Analysis

This chapter discusses the major challenges faced in engineering design and analysis. Going from an initial geometric design to a finite element mesh constitutes the most time-consuming step of the overall design through analysis process. The concept of isogeometric analysis has thus far addressed this issue by utilizing the NURBS functions commonly found in CAD packages as an isoparametric basis for both the geometry and the solution space. We extend the methodology to include T-splines, a technology rapidly gaining favor in the geometry community due to its flexibility and efficiency in representing complex objects. This efficiency stems from its locally refinable basis, a feature ideally suited to finite element analysis where local refinement is frequently desirable. Examples are presented.