An adaptive isogeometric-meshfree coupling approach for the limit analysis of cracked structures

Abstract

An adaptive isogeometric-meshfree (AIMF) coupling approach is proposed to predict the limit load factors of cracked structures. The concept of the present approach, which relies on forming an equivalence between the isogeometric analysis (IGA) and moving least-squares meshfree method, is developed based on the reproducing conditions, resulting in a unified formulation of the basis functions. Thereby, the refinement of IGA can be implemented in a straightforward meshfree manner for limit analysis problems. The adaptivity of refinement is realized by adopting an indicator of plastic dissipation to automatically identify the material regions associated with the dissipated work greater than a predefined threshold. Subsequently, the marked meshes are refined through the insertion of linear reproducing points. Enrichment functions are further introduced to the present approach for crack modelling. The resulting optimization formulation of limit analysis is re-expressed in the form of second-order cone programming which can be effectively tackled by the interior-point solvers. Through a series of numerical examples, the present approach has been proven to achieve both high convergence rates and accurate simulation results.