Adaptive multi-patch isogeometric analysis with truncated hierarchical B-splines in isotropic/orthotropic media

Abstract

We present an adaptive multi-patch isogeometric analysis on the basis of truncated hierarchical B-splines (THB-splines) for solving two-dimensional complex isotropic/orthotropic elasticity. The THB-splines have local refinement property and their basis functions exhibit linear independence, so these features are highly applicable for adaptive isogeometric analysis. Guided by a posterior error estimator based on stress recovery, the adaptive algorithm is utilized in isogeometric analysis. In order to further extend the proposed method to solve complex geometry problems, the multi-patch technique is adopted to achieve exact modeling with Nitsche’s method as a multi-patch coupling approach. An isotropic numerical example with exact analytical solutions and three orthotropic numerical examples are presented to verify the effectiveness and accuracy of the developed method. Numerical solutions show that the developed adaptive isogeometric analysis method has high computational efficiency.