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SCIENCE CHINA Technological Sciences, Volume 61 , Issue 6 : 923-933(2018) https://doi.org/10.1007/s11431-017-9143-9

An h-adaptive numerical manifold method for solid mechanics problems

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  • ReceivedJun 13, 2017
  • AcceptedAug 31, 2017
  • PublishedNov 21, 2017

Abstract

The numerical manifold method (NMM) features its dual cover systems, namely the mathematical cover and physical cover, which provide a unified framework for mechanics problems involving continuum and discontinuum deformation. Uniform finite element meshes can be and are usually used to construct the mathematical cover. Though this strategy can handle different kinds of problems in a unified way, it is not economical for cases with steep deformation gradients or singularities. In this paper, using the recovery-based error estimator, an h-adaptive NMM on quadtree meshes is proposed to deal with such cases. The quadtree meshes serve as the mathematical meshes, on which the local refinement is carried out. When the quadtree meshes are refined, the corresponding mathematical cover, physical cover and manifold elements are updated accordingly. To handle the hanging nodes in the quadtree meshes, we resort to mean value coordinates. Comparing to the refinement based on manifold elements, the proposed strategy guarantees consistent structured meshes throughout the adaptive process, thus retaining the unique feature of original NMM. In contrast with polygonal finite element method, an advantage of the proposed method is that the meshes do not need to conform to the crack face and material boundary, which means the adaptive NMM is very suitable for problems with complex geometric boundary. Several representative mechanics problems, including crack problems, are analyzed to investigate the effectiveness of the proposed method. It is demonstrated that the proposed adaptive NMM has higher accuracy and better performance comparing to uniform refinement strategy.


Funded by

National Natural Science Foundation of China(11602165 ,&, 51479131)

Open Research Fund of State Key Laboratory of Geome-chanics and Geotechnical Engineering

Institute of Rock and Soil Mechanics

Chinese Academy of Sciences(Z015010)

Natural Science Fund of Tianjin City(16JCQNJC07800)


Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11602165 & 51479131), Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences (Grant No. Z015010), and the Natural Science Fund of Tianjin City (Grant No. 16JCQNJC07800).


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