We present a method for isogeometric analysis on a triangulation of a domain bounded by NURBS curves. In this method, both the geometry and... Show moreWe present a method for isogeometric analysis on a triangulation of a domain bounded by NURBS curves. In this method, both the geometry and the physical eld are represented by bivariate splines in Bernstein B ezier form over the triangulation. We describe a set of procedures to construct a parametric domain and its triangulation from a given physical domain, construct Cr-smooth basis functions over the domain, and establish a rational Triangular B ezier Spline (rTBS) -based geometric mapping that Cr smoothly maps the parametric domain onto the physical domain and exactly recovers NURBS boundaries. As a result, this approach can achieve automated meshing of objects with complex topologies and allows highly localized re nement. Isogeometric analysis of problems from linear elasticity and advectiondi usion analysis are demonstrated. M.S. in in Mechanical Engineering, May 2013 Show less
