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Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress
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摘要 A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig_3-CNS(NMM)element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig_3-CNS(NMM) element can be considered as a development of both the Trig_3-CNS element and the numerical manifold method(NMM).Inheriting all the advantages of Trig_3-CNS element, calculations using Trig_3-CNS(NMM) element can obtain higher accuracy than Trig_3 element without extra degrees of freedom(DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig_3-CNS(NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper,complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig_3-CNS(NMM) element. Numerical results show that the Trig_3-CNS(NMM) element is prominent in modeling complex crack problems. A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig3-CNS (NMM) element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig3-CNS (NMM) element can be considered as a development of both the Trig3-CNS element and the numerical manifold method (NMM). Inheriting all the advantages of Trig3-CNS element, calculations using Trig3-CNS (NMM) element can obtain higher accuracy than Trig3 element without extra degrees of freedom (DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig3-CNS (NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper, complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig3-CNS (NMM) element. Numerical results show that the Trig3-CNS (NMM) element is prominent in modeling complex crack problems.
作者 YANG YongTao XU DongDong SUN GuanHua ZHENG Hong Yang YongTao[1];Xu DongDong[2];Sun GuanHua[1];Zheng Hong[3]
出处 《中国科学:技术科学英文版》 SCIE EI CAS CSCD 2017年第10期1537-1547,共11页 SCIENCE CHINA Technological Sciences
基金 This work was supported by the National Natural Science Foundation of China (Grant Nos. 51609240, 11572009 & 51538001), and the National Basic Research Program of China (Grant No. 2014CB047100).
关键词 数值流形方法 三角形单元 节点应力 裂纹问题 拟合 中枢神经系统 裂缝问题 NMM numerical manifold method, Trig3-CNS (NMM) element, stress intensity factor, complex crack problems
作者简介 Corresponding author (email: ghsun@whrsm.ac.cn)
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