Adaptive analysis of crack propagation in thin-shell structures via an isogeometric-meshfree moving least-squares approach

Abstract

This paper reports an isogeometric-meshfree moving least-squares approach for the adaptive analysis of crack propagation in thin-shell structures within the context of linear elastic fracture mechanics. The present approach is developed based on the equivalence of the moving least-squares meshfree shape functions and the isogeometric basis functions, which provides an effective strategy of adaptive mesh refinement for isogeometric analysis (IGA) in a straightforward meshfree manner. The adaptivity of the mesh refinement is achieved by utilizing a gradient-based error estimator to identify the meshes that need to be refined by adding linear reproducing points. The Kirchhoff–Love theory is further applied in the isogeometric-meshfree moving least-squares formulation to simplify the modeling of cracked thin-shell structures by neglecting the rotational degrees of freedom. In this way, the singularity of stress fields near the crack tip and the discontinuity of displacement fields around the crack surface can be efficiently captured by the adaptive mesh refinement to generate accurate results. A series of two-dimensional static and quasi-static crack propagation problems of thin-shell structures are investigated. It is found that the adaptive refinement strategy makes the present approach achieve higher convergence rate and computational efficiency than IGA and the meshfree method. The predicted propagation paths obtained by the present approach are in good agreement with the previously reported results.