Crack Propagation by Element-Free Galerkin Methods
Abstract
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 15, 1997
- Accession Number
- ADA329723
Entities
People
- Ted Belytschko
Organizations
- Northwestern University