##
**Efficient calculation of internal results in 2D elasticity BEM.**
*(English)*
Zbl 1182.74214

Summary: The solution of boundary integral equations in their discretized form requires an accurate treatment of regular as well as singular integrals. The regular integrals are usually solved numerically using Gauss quadrature. Since these integrations make up the major part of the numerical work the choice of the appropriate Gauss order is essential to an accurate and efficient boundary element analysis. Thus, a considerable number of publications is dealing with the subject of choosing a Gauss order suitable to gain efficiency without loosing accuracy. The guidelines determining the choice of the appropriate Gauss order is usually called an integration criterion. This paper presents a study on this topic with emphasis on the accuracy of internal results in 2D elasticity. First the necessity for a new integration criterion is shown. Then a new criterion is derived. This new criterion and various existing criteria from the literature are applied to a standard benchmark problem. The superior performance of the novel criterion is demonstrated.

### MSC:

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

74B05 | Classical linear elasticity |

### Keywords:

boundary element method; error bound estimate; adaptive integration scheme; numerical integration### Software:

BEMECH
PDF
BibTeX
XML
Cite

\textit{U. Eberwien} et al., Eng. Anal. Bound. Elem. 29, No. 5, 447--453 (2005; Zbl 1182.74214)

Full Text:
DOI

### References:

[1] | Aliabadi, M.H., The boundary element methodâ€”applications in solids and structures, (2002), Wiley UK · Zbl 0994.74003 |

[2] | Beer, G., Programming the boundary element method, (2001), Wiley UK |

[3] | Jun, L.; Beer, G.; Meek, J.L., Efficient evaluation of integrals of order 1/r, 1/r2, 1/r3 using Gauss quadrature, Eng anal bound elem, 2, 3, 118-123, (1985) |

[4] | Bu, S.; Davies, T.G., Effective evaluation of non-singular integrals in 3D BEM, Adv eng software, 23, 121-128, (1995) |

[5] | Cruse, T.A.; Aithal, R., Non-singular boundary integral equation implementation, Int J numer eng, 36, 237-254, (1993) |

[6] | Gao, X.W.; Davies, T.G., Boundary element programming in mechanics, (2002), Cambridge University Press UK |

[7] | Hayami, K.; Matsumoto, H., A numerical quadrature for nearly singular boundary element integrals, Eng anal bound elem, 13, 143-154, (1994) |

[8] | Lachat, J.C.; Watson, J.O., Effective numerical treatment of boundary integral equations: a formulation for three-dimensional elastostatics, Int J numer methods eng, 10, 991-1005, (1976) · Zbl 0332.73022 |

[9] | Schulz, H.; Schwab, C.; Wendland, W.L., The computation of potentials near and on the boundary by an extraction technique for boundary element methods, Comput methods appl mech eng, 157, 225-238, (1998) · Zbl 0943.65138 |

[10] | Stroud, A.H.; Secrest, D., Gaussian quadrature formulae, (1966), Prentice Hall Englewood Cliffs · Zbl 0156.17002 |

[11] | Telles, J.C.F., A self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals, Int J numer methods eng, 24, 953-973, (1978) |

[12] | Wrobel, L.C., The boundary element method, (2002), Wiley UK |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.