Premium
DYNAMIC FRACTURE USING ELEMENT‐FREE GALERKIN METHODS
Author(s) -
BELYTSCHKO T.,
TABBARA M.
Publication year - 1996
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/(sici)1097-0207(19960330)39:6<923::aid-nme887>3.0.co;2-w
Subject(s) - galerkin method , quadratic equation , moving least squares , fracture mechanics , mathematics , stress intensity factor , point (geometry) , mathematical analysis , finite element method , mathematical optimization , structural engineering , geometry , engineering
The element‐free Galerkin method for dynamic crack propagation is described and applied to several problems. This method is a gridless method, which facilitates the modelling of growing crack problems because it does not require remeshing; the growth of the crack is modelled by extending its surfaces. The essential feature of the method is the use of moving least‐squares interpolants for the trial‐and‐test functions. In these interpolants, the dependent variable is obtained at any point by minimizing a weighted quadratic form involving the nodal variables within a small domain surrounding the point. The discrete equations are obtained by a Galerkin method. The procedures for modelling dynamic crack propagation based on dynamic stress intensity factors are also described.