Multi-inclusions modeling by adaptive XIGA based on LR B-splines and multiple level sets

In this paper, we present an effective computational approach that combines an adaptive extended isogeometric analysis (XIGA) method with locally refined (LR) B-splines and level set methods for modeling multiple inclusions in two-dimensional (2D) elasticity problems. The advantage of XIGA is to mod...

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Bibliographic Details
Published in:Finite elements in analysis and design 2018-09, Vol.148, p.48-66
Main Authors: Gu, Jiming, Yu, Tiantang, Van Lich, Le, Nguyen, Thanh-Tung, Tanaka, Satoyuki, Bui, Tinh Quoc
Format: Article
Language:English
Subjects:
Adaptivity
CAD
Computer aided design
Crack propagation
Elasticity
Error estimation
Finite element analysis
Finite element method
Geometry
Grid refinement (mathematics)
Inclusions
Level set
Locally refined B-splines
Materials elasticity
Mathematical models
Microstructure
Multiple inclusions
Splines
Two dimensional models
XIGA
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Summary:In this paper, we present an effective computational approach that combines an adaptive extended isogeometric analysis (XIGA) method with locally refined (LR) B-splines and level set methods for modeling multiple inclusions in two-dimensional (2D) elasticity problems. The advantage of XIGA is to model inclusions without considering internal inclusion interfaces by additional functions. Multiple level set functions are used to represent the location of inclusion interfaces and to define enrichment functions. Local refinement for adaptive XIGA using LR B-splines is based on the posterior error estimator. We use the strategy of structured mesh refinement to implement local refinement in adaptive XIGA. Numerical experiments for multiple inclusions with complicated geometries are presented to demonstrate the accuracy and performance of the proposed approach. In addition, numerical results indicate that the adaptive XIGA with local refinement achieves faster convergence rate than that of the XIGA with uniform global refinement. •An adaptive XIGA method with multiple level sets is presented for multiple inclusions in 2D elasticity.•Multiple level set functions are used to represent the location of inclusion interfaces.•A posterior error estimation methodology for adaptive XIGA using LR B-splines is provided.•Local refinement is performed according to the posterior error estimation based on recovery.•Numerical examples verify effectiveness and accuracy of the proposed adaptive XIGA method for multiple inclusions.
ISSN:0168-874X
1872-6925
DOI:10.1016/j.finel.2018.05.003