A NEW IMPLEMENTATION OF THE ELEMENT FREE GALERKIN METHOD

Element free Galerkin methods (EFG) are methods for solving partial differential equations with moving least squares interpolants. EFG methods require only nodal data; no element connectivity is needed. In a previous implementation of the EFG method, Lagrange multipliers were used to enforce the essential boundary condition. However, the use of Lagrange multipliers increases the cost of solving the linear algebraic equations. A new implementation 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; the latter makes it very advantageous for modelling progressive cracking.