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**Boundary element-free method (BEFM) and its application to two-dimensional elasticity problems.**
*(English)*
Zbl 1147.74047

Summary: 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 |

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

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