T-Spline Based Local Refinement for Mesh Independent Analysis

Structured background mesh with regular shaped uniform elements is easy to generate automatically. Analysis using such a mesh is possible with an independent CAD model representing the geometry by using Implicit Boundary Method. This avoids mesh generation difficulties and enables new types of elements that use B-spline approximations instead of the traditional Lagrange interpolations. But the background mesh should ideally have higher resolution in areas where the solution has large gradients. In this paper, T-spline basis functions are used to locally refine a structured mesh. T-splines allow construction of elements with T-junctions maintaining the continuity of the field variable across element boundaries and hence ensure that compatibility conditions are satisfied. T-spline elements are constructed for linear and cubic basis. Essential boundary conditions are applied using implicit boundary method, which allows boundary conditions to be imposed even when there are no nodes on the boundary. T-spline elements are shown to represent constant and linear solution exactly. The mesh refinement technique is evaluated using two dimensional elasticity problem involving stress concentration.