Analysis-suitable T-splines

In the processes of engineering design and analysis, there are some integration problems of design and finite element analysis. While iso-geometric analysis(IGA) uses the smooth spline basis that define the geometry basis for analysis, which provides the possibility for integration problems. T-splines have emerged as an important technology for IGA and have been used to solve many limitations inherent in the non-uniform ra-tional B-splines(NURBS) representation. The main typical properties for T-splines are local refinement, watertightness via merging and trimmed NURBS conversion. How-ever, the whole class of T-splines are not suitable for IGA since not all of them have linearly independent blending functions. Thus, AST-splines were developed in [117] to meet the basic needs for IGA. Most of the articles focus on the bi-cubic AST-splines, so we generalize bi-cubic degree to any bi-degrees. And we derive a recursive relation for AST-splines and use the relation to prove the partition of unity property for AST-splines.The knot insertion and degree elevation algorithms are two main fundamental algo-rithms which are used to enrich a spline space. Degree elevation For NURBS has been well studied, while no articles focus on the degree elevation algorithm for T-splines. We develop a recursive algorithm for general T-spline degree elevation and develop two analysis-suitable T-spline degree elevation,that could also help to develop the IGA application.Among the basic properties, linear independence is one of the most priori ones for IGA. There is a fact that a bilinear T-spline defined on a T-mesh without L-junctions has linear independent blending functions. A T-mesh has no L-junctions doesn’t hASTo be an AST-mesh. So we find out semi-analysis-suitable T-splines which is a more general class of T-splines and shows that the blending functions for any such T-spline are linearly independent regardless of knot intervals. And depending on this kind of T-splines, we also present an optimized refinement algorithm for T-splines to make sure that the new T-splines after refinement have linearly independent blending functions.