A NEW IMPLEMENTATION OF THE ELEMENT FREE GALERKIN METHOD

Element free Galerkin methods (EFG) are methods for solving partial di fferential equations with moving least squares interpolants. EFG metho ds require only nodal data; no element connectivity is needed. In a pr evious implementation of the EFG method, Lagrange multipliers were use d to enforce the essential boundary condition. However, the use of Lag range multipliers increases the cost of solving the linear algebraic e quations. A new implementation is developed based on a modified variat ional principle in which the Lagrange multipliers are replaced at the outset by their physical meaning so that the discrete equations are ba nded. In addition, weighted orthogonal basis functions are constructed so the need for solving equations at each quadrature point is elimina ted. Numerical examples show that the present implementation effective ly computes stress concentrations and stress intensity factors at crac ks with very irregular arrangements of nodes; the latter makes it very advantageous for modelling progressive cracking.