MIAO Yu, WANG Yuan-han. Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method[J]. Applied Mathematics and Mechanics, 2006, 27(5): 597-604.
 Citation: MIAO Yu, WANG Yuan-han. Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method[J]. Applied Mathematics and Mechanics, 2006, 27(5): 597-604.

# Meshless Analysis for Three-Dimensional Elasticity With Singular Hybrid Boundary Node Method

• Rev Recd Date: 2006-02-10
• Publish Date: 2006-05-15
• The singular hybrid boundary node method (SHBNM) is proposed for solving threedimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The ‘boundary layer effect', which is the main drawback of the original hybrid BNM, was overcomed by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3-D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples.
•  [1] Lucy L B.A numerical approach to the testing of the fission hypothesis[J].Astronomic Journal,1977,18(12):1013—1024. [2] Belytschko T,Lu Y Y,Gu L.Element-free Galerkin methods[J].International Journal for Numerical Methods in Engineering,1994,137(2):229—256. [3] Mukherjee Y X,Mukherjee S.The boundary node method for potential problems[J].International Journal for Numerical Methods in Engineering,1994,40(5):797—815. [4] Zhang J M,Yao Z H,Li H.A hybrid boundary node method[J].International Journal for Numerical Methods in Engineering,2002,53(5):751—763. doi: 10.1002/nme.313 [5] Zhang J M,Yao Z H.The meshless regular hybrid boundary node method for 2D linear elasticity[J].Engineering Analysis With Boundary Elements,2003,27(3):259—268. [6] DeFigueredo T G B, Brebbia C A.A new hybrid displacement variational formulation of BEM for elastostatics[A].In: Brebbia C A, Conner J J, Eds.Advances in Boundary Elements[C].Southampton: Computational Mechanics Publication,1989,1(1):47—57. [7] Atluri S N, Kim H G,Cho J Y.A critical assessment of the truly meshless local Petrov-Galerkin (MLPG),and local boundary integral equation (LBIE) methods[J].Computational Mechanics,1999,24(2):348—372.

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