Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems.

*(English)*Zbl 1147.74047Summary: We discuss the moving least-square approximation (MLS) method. In some cases, the MLS may form an ill-conditioned system of equations, so that the solution cannot be correctly obtained. Hence, in this paper we propose an improved moving least-square approximation (IMLS) method. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and accuracy than the MLS, and will not lead to ill-conditioned systems of equations. Combining the boundary integral equation (BIE) method and the IMLS approximation method, a direct meshless BIE method, the boundary element-free method (BEFM), is presented for two-dimensional elasticity. Compared to other meshless BIE methods, BEFM is a direct numerical method in which the basic unknown quantity is the real solution for nodal variables, and boundary conditions can be applied easily; hence, it has higher computational accuracy. For demonstration purpose, we give selected numerical examples.

##### MSC:

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

74B05 | Classical linear elasticity |

PDF
BibTeX
XML
Cite

\textit{K. M. Liew} et al., Int. J. Numer. Methods Eng. 65, No. 8, 1310--1332 (2006; Zbl 1147.74047)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Beer, International Journal forNumerical Methods in Engineering 28 pp 1233– (1989) |

[2] | Beer, International Journal forNumerical Methods in Engineering 36 pp 3579– (1993) |

[3] | Tabatabai-Stocker, Communications in Numerical Methods in Engineering 14 pp 355– (1998) · Zbl 0906.73075 |

[4] | Liew, International Journal for Numerical Methods in Engineering 56 pp 2331– (2003) |

[5] | Liew, International Journal for Numerical Methods in Engineering 57 pp 599– (2003) |

[6] | Liew, International Journal for Numerical Methods in Engineering 60 pp 1861– (2004) |

[7] | Liew, International Journal for Numerical Methods in Engineering 63 pp 1014– (2005) |

[8] | Belytschko, Computer Methods in Applied Mechanics and Engineering 139 pp 3– (1996) |

[9] | Lancaster, Mathematics of Computation 37 pp 141– (1981) |

[10] | Liew, International Journal for Numerical Methods in Engineering 56 pp 2331– (2003) |

[11] | Liew, International Journal for Numerical Methods in Engineering 57 pp 599– (2003) |

[12] | Gu, Computer Methods in Applied Mechanics and Engineering 190 pp 4405– (2001) |

[13] | Mukherjee, International Journal for Numerical Methods in Engineering 40 pp 797– (1997) |

[14] | Chati, International Journal for Numerical Methods in Engineering 46 pp 1163– (1999) |

[15] | Chati, International Journal for Numerical Methods in Engineering 47 pp 1523– (2000) |

[16] | Zhu, Computational Mechanics 21 pp 223– (1998) |

[17] | . Theory of Elasticity (3rd edn). McGraw-Hill: New York, 1970. |

[18] | Elementary Fracture Mechanics (3rd edn). Martinus Nijhoff: The Hague, 1982. |

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.