Application of relations of singularity intensities of tangent derivatives of boundary displacements and tractions to BEM.

*(English)*Zbl 1244.74197Summary: In order to obtain a highly accurate numerical solution for a two-dimensional elasticity problem with singular boundary conditions on the smooth surface of an elastic body by boundary element method (BEM), the continuous or the singular requirements of the boundary field variables and their derivatives at element intersections have to be satisfied. The singularity intensities of the unknown boundary field variables have been determined through the theoretical relations of singularity intensities of tangent derivatives of boundary displacements and tractions, a priori. The continuous or singular requirements of boundary field variables and their derivatives at element intersections are automatically satisfied by using single node quadratic element (SNQE) developed in this paper. An example problem with singular boundary conditions on the surface of a semi-infinite-plane is numerically studied by BEM by using traditional three-nodes isoparametric elements and SNQEs. Numerical results show that the computation precisions at singular boundary points are greatly increased by using SNQEs.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74B05 | Classical linear elasticity |

74G70 | Stress concentrations, singularities in solid mechanics |

##### Keywords:

BEM; single node quadratic element; discontinuity of the first kind; lnr weak singularity; derivative of boundary displacement; traction
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\textit{Ch. Wang} and \textit{Z. L. Li}, Eng. Anal. Bound. Elem. 33, No. 5, 618--626 (2009; Zbl 1244.74197)

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##### References:

[1] | Brebbia, C.A.; Telles, J.C.F.; Wrobel, L.C., Boundary element techniques, (1984), Springer New York · Zbl 0556.73086 |

[2] | Williams, M.L., Stress singularities resulting from various boundary conditions in angular comers of plates in extension, J appl mech, 19, 526-528, (1952) |

[3] | England, A.H., On stress singularities in linear elasticity, Int J eng sci, 9, 571-585, (1971) · Zbl 0219.73005 |

[4] | Rösel, R., On the wedge notch eigenvalues, Int J fract., 33, 61-67, (1987) |

[5] | Ting, T.C.T., The wedge subjected to tractions: A paradox re-examined, J elasticity, 14, 235-247, (1984) · Zbl 0568.73015 |

[6] | Wang, M.Z., The wedge subjected to general tractions: A paradox resolved, Acta mech sin, 18, 243-252, (1986), [in Chinese] · Zbl 0607.73020 |

[7] | Li ZL, Wang Ch. Theoretical relations of boundary displacement derivatives and tractions at a singular boundary point for 2D isotropic elastic problems. Acta Mech Solida Sin., to appear. |

[8] | Ligget, J.A.; Salmon, J.R., Cubic spline boundary elements, Int J num methods eng, 17, 453-556, (1981) |

[9] | Walters, H.G.; Oritiz, J.C.; Gipson, G.S.; Brewer, J.A., Overhouser boundary elements in potential theory and linear elastostatics, (), 459-464 |

[10] | Watson, J.O., Hermitian cubic boundary elements for the analysis of cracks of arbitrary geometry, (), 465-474 |

[11] | Li, Z.L.; Zhan, F.L.; Du, S.H., A highly accurate BEM in fracture mechanics, Key eng mater, 183, 91-96, (2000) |

[12] | Ke, L.; Wang, Ch.; Zhan, F.L., BEM with single-node quadratic element in crack analysis, Acta mech solida sin, 54-64, (2002) |

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