Multi-patch local mesh refinement XIGA based on LR NURBS and Nitsche’s method for crack growth in complex cracked plates

Published on Jun 1, 2021in Engineering Fracture Mechanics3.426
· DOI :10.1016/J.ENGFRACMECH.2021.107780
Hongting Yuan2
Estimated H-index: 2
(Hohai University),
Tiantang Yu32
Estimated H-index: 32
(Hohai University),
Tinh Quoc Bui54
Estimated H-index: 54
(TITech: Tokyo Institute of Technology)
Source
Abstract
Abstract The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partition of unity, thus it is convenient in modeling evolution of crack. The locally refined non-uniform rational B-splines (LR NURBS), which have the properties of local refinement and exact description of geometry, are used to construct geometric model and taken as the shape functions in XIGA. To implement the adaptive local refinement, a method based on recovery technique by Zienkiewicz and Zhu is proposed. Based on the Mindlin–Reissner plate theory, interaction integral method is employed to calculate stress intensity factors (SIFs) and the maximum circumferential stress criterion is used to determine the crack propagation direction. Several numerical examples are carried out to demonstrate the performance of the adaptive multi-patch XIGA for simulating crack growth in complex plates.
References54
Newest
#1Davide D’Angella (TUM: Technische Universität München)H-Index: 5
#2Alessandro Reali (UNIPV: University of Pavia)H-Index: 45
Abstract The main motivation for hierarchical B-Splines in Isogeometric Analysis is to perform a local refinement that is globally not a tensor product. Compared to standard knot insertion, this allows to increase refinement locality. Moreover, the implementation of hierarchical refinement on existing codes can be facilitated by Bezier extraction. This approach was initially developed for unrefined patches and then extended to local refinement. In case of B-Spline patches that are not locally re...
Source
#1Keke Li (Hohai University)H-Index: 1
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 3 authors...
Abstract Limit analysis, without the complicated elasto-plastic computation, is an efficient method for estimating safety load of engineering structures. This paper develops a novel computational approach by integrating second-order cone programming (SOCP) into adaptive extended isogemetric elements (XIGA) for upper-bound limit analysis of cracked structures. The advantage of XIGA is to model cracks without considering the location of crack faces by introducing enrichment functions. The local re...
1 CitationsSource
#1Tiantang Yu (Hohai University)H-Index: 32
#2Hongting Yuan (Hohai University)H-Index: 2
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 5 authors...
Abstract This paper presents an error-controlled adaptive extended isogeometric analysis (XIGA) for assessment of fracture behavior for through-cracked Mindlin-Reissner plates. The locally refined (LR) B-splines that facilitate the local refinement are used as the basis functions for the approximations, while the kinematics of plates are described in terms of the Mindlin-Reissner plate theory. Appropriate enrichment functions for cracked plates are incorporated into the formulation to represent ...
9 CitationsSource
#1Weidong Li (NTU: Nanyang Technological University)H-Index: 6
#2Nhon Nguyen-Thanh (NTU: Nanyang Technological University)H-Index: 21
Last. Kun Zhou (NTU: Nanyang Technological University)H-Index: 61
view all 3 authors...
Abstract A strong form-based isogeometric-meshfree moving least-squares collocation (IMMLS-C) approach is developed for two-dimensional linear elastic fracture problems with contact loading. The IMMLS-C approach uses reproducing conditions to establish an equivalence between MLS shape functions and isogeometric basis functions. The advantages of this approach include the exact geometry representation, convenient crack modeling and flexible adaptive refinement. The IMMLS-C approach focuses on sol...
5 CitationsSource
#1Paola Gervasio (University of Brescia)H-Index: 12
#2Federico Marini (National Research Council)H-Index: 1
In this paper we apply the INTERNODES method to solve second order elliptic problems discretized by Isogeometric Analysis methods on non-conforming multiple patches in 2D and 3D geometries. INTERNODES is an interpolation-based method that, on each interface of the configuration, exploits two independent interpolation operators to enforce the continuity of the traces and of the normal derivatives. INTERNODES supports non-conformity on NURBS spaces as well as on geometries. We specify how to set u...
Source
#1Zhilin Han (Donghua University)H-Index: 3
#2Changzheng Cheng (Hefei University of Technology)H-Index: 10
Last. Zhongrong Niu (Hefei University of Technology)H-Index: 11
view all 4 authors...
Abstract To describe the physical fields of the V-notch structure accurately, the structure is first divided into two parts, the notch tip sector containing singular stress field and the non-singular remained part. A twofold procedure is then carried out to obtain the stress intensity factors: (I) the asymptotic expansions are introduced to describe physical fields of the singular region and transform the elastic governing equation to the characteristic ordinary differential equations. The inter...
4 CitationsSource
#1Jiming Gu (Hohai University)H-Index: 7
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 6 authors...
Abstract This paper is concerned with the numerical investigation of fracture mechanics parameters for cracked orthotropic composite structures by using an efficient computational approach. The adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines is thus developed. This adaptive XIGA is enhanced by both signed-distance and orthotropic crack-tip enrichment functions to represent strong discontinuity and singularity induced by crack, respectively. In addition, to ...
13 CitationsSource
#1Jiming Gu (Hohai University)H-Index: 7
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 54
view all 6 authors...
Abstract This paper aims at investigating fracture behavior of single and multiple cracks in two-dimensional solids by an adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines. The adaptive XIGA is capable of modeling cracks without considering the location of crack faces due to the local enrichment technique based on partition-of-unity concept. The XIGA approximation is locally enriched by Heaviside function and crack tip enrichment functions to capture the disc...
15 CitationsSource
#1H.S. Yang (BIT: Beijing Institute of Technology)H-Index: 3
#1H.S. Yang (BIT: Beijing Institute of Technology)H-Index: 2
Last. Chunying Dong (BIT: Beijing Institute of Technology)H-Index: 18
view all 2 authors...
Abstract In this paper, a posteriori error estimation and mesh adaptation approach for thin plate and shell structures of through-the-thickness crack is presented. This method uses the extended isogeometric analysis (XIGA) based on PHT-splines (Polynomial splines over Hierarchical T-meshes), which is abbreviated as XIGA-PHT. In XIGA-PHT, the isogeometric displacement approximation is locally enriched with enrichment functions, which efficiently capture the displacement discontinuity across the c...
12 CitationsSource
#1Shuohui Yin (XTU: Xiangtan University)H-Index: 18
#2Tiantang Yu (Hohai University)H-Index: 32
Last. Shuitao Gu (Chongqing University)H-Index: 3
view all 5 authors...
Abstract The main objective of this paper is to develop a novel multiscale approach for simulating static and stationary dynamic crack problems in two-dimensional elastic solids through an extended isogeometric analysis using the Non-Uniform Rational B-Splines (NURBS). This multiscale strategy consists of two techniques that the Nitsche’s method is applied for coupling different length-scales meshes on one hand, and on the other hand, a local enrichment technique is taken to describe the cracks ...
16 CitationsSource
Cited By0
Newest