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**Coupling of the improved element-free Galerkin and boundary element methods for two-dimensional elasticity problems.**
*(English)*
Zbl 1244.74204

Summary: In this paper, the element-free Galerkin (EFG) method and improved moving least-squares (IMLS) approximation are combined. An improved FEG (IEFG) method for two-dimensional elasticity is discussed, and the coupling of the IEFG method and the boundary element method (BEM) is presented. In the IMLS approximation, an orthogonal function system with a weight function is used as the basis function. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation, and does not lead to an ill-conditioned system of equations. There are fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method that is formed with the IMLS approximation fewer nodes are selected in the entire domain than are selected using the conventional EFG method. Hence, the IEFG method should result in a higher computing speed. Based on the IMLS approximation and the IEFG method, a direct coupling of the IEFG method and the BEM is discussed for two-dimensional elasticity problems, and the corresponding formulae of the coupled method are obtained. The coupled method does not need a new sub-domain between the IEFG method and the BEM sub-domains. Selected numerical examples are solved using the coupled method.

### MSC:

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

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74B05 | Classical linear elasticity |

### Keywords:

improved moving least-squares (IMLS) approximation; meshless method; element-free Galerkin (EFG) method; improved FEG (IEFG) method; boundary element method; elasticity
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\textit{Z. Zhang} et al., Eng. Anal. Bound. Elem. 32, No. 2, 100--107 (2008; Zbl 1244.74204)

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