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A new implementation of the element free Galerkin method. (English) Zbl 0847.73064
A new implementation of the element free Galerkin method is developed based on a modified variational principle in which the Lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are banded. In addition, weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is eliminated. Numerical examples show that the present implementation effectively computes stress concentrations and stress intensity factors at cracks with very irregular arrangements of nodes.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74R99 Fracture and damage
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