Adaptive analysis of three-dimensional structures using an isogeometric control net refinement approach

A new approach for the adaptive isogeometric solution of three-dimensional elasticity problems is presented. The error energy norms are calculated by isogeometric analysis, and the share of each control point from its vicinity is assigned by using Voronoi tessellation. Then, the net of control points is imagined as a hypothetical truss-like structure subject to artificial thermal gradients proportional to the control point errors. Analyzing this structure under the temperature variations, a new arrangement of control points is obtained. Repeating consequent isogeometric and thermo-elastic analyses will eventually lead to a better distribution of errors in the domain of problem and results in an optimal net of control points. To demonstrate the performance and efficiency of the proposed method, a few examples are presented. The obtained results indicate that this innovative approach is effective in reducing errors of three-dimensional problems and can be employed for improving solution accuracy in the context of isogeometric analysis approach.