Element-free Galerkin method for wave propagation and dynamic fracture.

*(English)*Zbl 1067.74599Summary: The element-free Galerkin method (EFG) is extended to dynamic problems. The EFG method, which is based on moving least square interpolants, requires only nodal data; no element connectivity is needed. This makes the method particularly attractive for moving dynamic crack problems, since remeshing can be avoided. In contrast to the earlier formulation for static problems by the authors, the weak form of kinematic boundary conditions for dynamic problems is introduced in the implementation to enforce the kinematic boundary conditions. With this formulation, the stiffness matrix is symmetric and positive semi-definite, and hence the consistency, convergence and stability analyses of time integration remain the same as those in the finite element method. Numerical examples are presented to illustrate the performance of this method. The relationship between the element-free Galerkin method and the smooth particle hydrodynamics method is also discussed in this paper. Results are presented for some one-dimensional and two-dimensional problems with static and moving cracks.

##### MSC:

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

74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |

74R99 | Fracture and damage |

##### Keywords:

moving least square interpolants; weak kinematic boundary conditions; smooth particle hydrodynamics
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\textit{Y. Y. Lu} et al., Comput. Methods Appl. Mech. Eng. 126, No. 1--2, 131--153 (1995; Zbl 1067.74599)

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