The improved element-free Galerkin method for two-dimensional elastodynamics problems.

*(English)*Zbl 1287.74055Summary: We derive an improved element-free Galerkin (IEFG) method for two-dimensional linear elastodynamics by employing the improved moving least-squares (IMLS) approximation. In comparison with the conventional moving least-squares (MLS) approximation function, the algebraic equation system in IMLS approximation is well-conditioned. It can be solved without having to derive the inverse matrix. Thus the IEFG method may result in a higher computing speed. In the IEFG method for two-dimensional linear elastodynamics, we employed the Galerkin weak form to derive the discretized system equations, and the Newmark time integration method for the time history analyses. In the modeling process, the penalty method is used to impose the essential boundary conditions to obtain the corresponding formulae of the IEFG method for two-dimensional elastodynamics. The numerical studies illustrated that the IEFG method is efficient by comparing it with the analytical method and the finite element method.

##### MSC:

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

74B05 | Classical linear elasticity |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

##### Keywords:

weighted orthogonal function; improved moving least squares (IMLS) approximation; improved element-free Galerkin (IEFG) method; elastodynamics; penalty method; Newmark-\(\beta\) algorithm##### Software:

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\textit{Z. Zhang} et al., Eng. Anal. Bound. Elem. 37, No. 12, 1576--1584 (2013; Zbl 1287.74055)

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