Extended isogeometric analysis based on PHT‐splines for crack propagation near inclusions

Abstract

Adaptive local refinement is one of the main issues for isogeometric analysis (IGA). In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T-meshes (PHT-splines) for modeling crack propagation is presented. The PHT-splines overcome certain limitations of nonuniform rational B-splines-based formulations; in particular, they make local refinements feasible.To drive the adaptive mesh refinement, we present a recovery-based error estimator for the proposed method. The method is based on the XIGA method, in which discontinuous enrichment functions are added to the IGA approximation and this method does not require remeshing as the cracks grow. In addition, crack propagation is modeled by successive linear extensions that are determined by the stress intensity factors under linear elastic fracture mechanics. The proposed method has been used to analyze numerical examples, and the stress intensity factors results were compared with reference results. The findings demonstrate the accuracy and efficiency of the proposed method.

An isogeometric‐meshfree coupling approach for analysis of cracks

“…where ij is the stress tensor components, ij is the strain tensor components, n j is the components of the unit normal vector to Γ, u i is the displacement components, and 1j is the Kronecker delta. By expanding and rearranging the terms in Equation 45, the following equation can be obtained:…”

“…Taking advantages of extended finite element method (XFEM) and IGA, extended IGA was developed for the fractural analysis. ()…”

“…39 Taking advantages of extended finite element method (XFEM) and IGA, extended IGA was developed for the fractural analysis. [40][41][42][43][44][45] In some previous research, the coupling method could be formed by several approaches including EFG with FEM/boundary element method (BEM) and the meshfree local Petrov-Galerkin with FEM/BEM. [46][47][48][49] Recently, the IGA has been incorporated with BEM and applied to elastostatics analysis, 50,51 acoustic problems, 51 posteriori error estimations for adaptive IGA-BEM, 52 and IGA-BEM for linear elastic fracture problems.…”

Weight‐adaptive isogeometric analysis for solving elastodynamic problems based on space‐time discretization approach

“…[21][22][23][24][25][26][27][28][29] This paper focuses on the numerical solution of two-dimensional (2D) elastodynamic problems by using a new and attractive method that is named weight-adaptive space-time discontinuous isogeometric analysis (WA-STDIGA). Before giving some additional explanations about the proposed approach, it is worthwhile to note that the IGA is a new powerful numerical method first proposed by Hughes et al 30 Dynamic and static analysis of plates and shells, [31][32][33][34][35] crack propagation analysis, 36,37 fluid mechanics, 38 and dynamic analysis of tall buildings 39 are only few samples where the IGA has been successfully used. In addition, in recent years, many articles have focused on the space-time formulation of IGA as an alternative method to space-time FEM.…”

Functional approach to the error control in adaptive IgA schemes for elliptic boundary value problems

“…However, in this case, one must assume the reduced regularity of basis [11] or fulfil a certain constraint on admissible mesh configuration [74]. In [47], the adaptive procedure in based on the recovery-based error estimator, in which discontinuous enrichment functions are added to the IgA approximation.…”