Adaptive multi-patch isogeometric analysis based on locally refined B-splines

Abstract

We present an effective adaptive analysis procedure in terms of isogeometric analysis (IGA) based on locally refined (LR) B-splines for two-dimensional elasticity problems. One major advantage of the adopted LR B-splines over B-splines and non-uniform rational B-splines (NURBS) is the local refinement, which makes it highly suitable for adaptive analysis. The Zienkiewicz–Zhu estimation is used on error estimator based local refinement. The local refinement is implemented by the structured mesh refinement strategy according to the posteriori error estimator. The proposed methodology is further extended to deal with multiple patches, which are applied to represent complicated shapes of structures, and the Nitsche’s method is employed for coupling patches among multiple patches in the present adaptive IGA. The algorithm for adaptive IGA on multiple patches is also derived. We provide a series of numerical examples for benchmarks and complicated configurations to demonstrate the flexibility and accuracy of the model as well as the significant enhancement in adaptive IGA based on LR B-splines. A careful comparison of the numerical results suggests that the adaptive local refinement strategy offers faster convergence rate than that of uniform refinement strategy.