Crack Propagation by Element-Free Galerkin Methods
Final rept. 1 Jan 94-31 Mar 97
NORTHWESTERN UNIV EVANSTON IL DEPT OF CIVIL ENGINEERING
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The element-free Galerkin EFG method is a mesh-free method for solving solid mechanics problems with an approximation based only on nodes. It is developed here for linear elastic fracture problems. Smoothing of mesh-free approximations near nonconvex boundaries is done by three methods 1 the diffraction method, in which the nodal domain of influence wrapped a short distance around a boundary, 2 the transparency method, which is described only for cracks, yields continuous approximations by gradually severing the domains of influence near crack tips, and 3 the see-through method, or continuous line criterion, which does not enforce a discontinuity or crack if the tip is within the domain of influence. Two methods for enriching EFG approximations for linear elastic fracture problems are described extrinsic enrichment involves adding the form of the solution to the trial function for intrinsic enrichment, the EFG basis is expanded to include terms from the near tip crack solution. Several problems are solved to illustrate the effectiveness of EFG crack propagation with smoothing and enrichment.