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The improved element-free Galerkin method for two-dimensional elastodynamics problems. (English) Zbl 1287.74055
Summary: 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
Software:
Mfree2D
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