Numerical simulation of arbitrary holes in orthotropic media by an efficient computational method based on adaptive XIGA

Abstract

We present in this paper an efficient computational approach based on an adaptive extended isogeometric analysis (XIGA) for simulation of arbitrary holes in orthotropic materials. The interfaces of holes are described by multiple level set functions so that the developed XIGA can capture the hole geometry without considering its interfaces. The approach is further enhanced by using the locally refined (LR) B-spline basis functions, which dominate over B-spline or non-uniform rational B-spline functions (NURBS) due to the local refinement. This study only deals with the structured mesh strategy for local refinement. The implementation of the local refinement is guided by posteriori error estimator based on stress recovery. Accuracy study is performed for isotropic media due to the availability of analytical solutions. For numerical experiments, different types of holes in orthotropic media are studied, and the computed numerical results are compared with reference solutions derived from ABAQUS (FEM). We also compare the convergence rate obtained by our adaptive local refinement with that derived from uniform global refinement to indicate the greater advantage of the developed adaptive XIGA.