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**A boundary element-free method (BEFM) for three-dimensional elasticity problems.**
*(English)*
Zbl 1109.74372

Summary: This study combines the boundary integral equation (BIE) method and improved moving least-squares (IMLS) approximation to present a direct meshless boundary integral equation method, the boundary element-free method (BEFM) for three-dimensional elasticity. Based on the improved moving least-squares approximation and the boundary integral equation for three-dimensional elasticity, the formulae of the boundary element-free method are given, and the numerical procedure is also shown. Unlike other meshless boundary integral equation methods, the BEFM is a direct numerical method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus giving it a greater computational precision. Three selected numerical examples are presented to demonstrate the method.

### MSC:

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

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

74B05 | Classical linear elasticity |

### Keywords:

Moving least-squares (MLS) approximation; improved moving least-squares (IMLS) approximation; weighted orthogonal function; weight function; compact support domain; boundary integral equation; meshless method; boundary element-free method (BEFM); elasticity### Software:

Mfree2D
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\textit{S. Kitipornchai} et al., Comput. Mech. 36, No. 1, 13--20 (2005; Zbl 1109.74372)

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### References:

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