SUMMARY The Element-Free Galerkin (EFG) method is a meshless method for solving partial di⁄erential equations which uses only a set of nodal points and a CAD-like description of the body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip, but stresses tend to be oscillatatory near the crack tip unless substantial refinement is used. An enriched EFG formulation for fracture problems is proposed. Two methods are used: (1) adding the asymptotic fields to the trial function and (2) augmenting the basis by the asymptotic fields. A local mapping of the enriched fields for curved cracks is also described. Results show that both methods greatly reduce stress oscillations and allow the calculation of accurate stress intensity factors with far fewer degrees of freedom. ( 1997 by John Wiley & Sons, Ltd.

Enriched element-free galerkin methods for crack tip fields

(1982). A LITERATURE SURVEY ON NUMERICAL HEAT TRANSFER. Numerical Heat Transfer: Vol. 5, No. 4, pp. 369-420.

A literature survey on numerical heat transfer

A new enriched finite element for fatigue crack growth

A size independent enriched finite element for the modeling of bimaterial interface cracks

This paper investigates interfacial cracks with arbitrary crack surface tractions. A novel singular finite element which is constructed with the analytical solution around interfacial cracks is presented. Interfacial crack problems can be analyzed numerically using the singular finite element, and Mode I and/or Mode II stress intensity factors can be obtained directly. Unlike other enriched elements for cracks, neither extra unknowns nor transition elements are required. Numerical examples are given to illustrate the validity of present method.

N. Muthiyalu

Papers

Least square and Galerkin finite element solution of flow past a flat plate

Least square finite element solution of stagnation point flow