A high order numerical manifold method and its application to linear elastic continuous and fracture problems  

作　　者：YANG YongTao SUN GuanHua CAI KeJian ZHENG Hong 

机构地区：[1]State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences [2]School of Civil and Transportation Engineering, NingBo University of Technology [3]Key Laboratory of Urban Security and Disaster Engineering, Ministry ofEducation, Beijing University of Technology

出　　处：《Science China(Technological Sciences)》2018年第3期346-358,共13页中国科学（技术科学英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.51609240&11572009);the Zhe Jiang Provincial Natural Science Foundation of China(Grant No.LY13E080009);the National Basic Research Program of China(Grant No.2014CB047100)

摘　　要：The numerical manifold method(NMM) is a partition of unity(PU) based method. For the purpose of obtaining better accuracy with the same mesh, high order global approximation can be adopted by increasing the order of local approximations(LAs). This,however, will cause the "linear dependence"(LD) issue, where the global matrix is rank deficient even after sufficient constraints are enforced. In this paper, through quadrilateral mesh to form the mathematical cover, a high order numerical manifold method called Quad4-COLS(NMM) is developed, where the constrained and orthonormalized least-squares method(CO-LS) is used to construct the LAs. The developed Quad4-COLS(NMM) does not need extra nodes or DOFs to construct high order global approximations, while is free from the LD issue. Nine numerical tests including five tests for linear elastic continuous problems and four tests for linear elastic fracture problems are carried out to validate the accuracy and robustness of the proposed Quad4-COLS(NMM).

关 键 词：partition of unity based methods numerical manifold method Quad4-COLS（NMM） crack propagation linear dependence 

分 类 号：O346.1[理学—固体力学]