Nodal integration of the element-free Galerkin method

Spatial integration of the element-free Galerkin (EFG) method is achieved by evaluating the integrals of the weak form only at the nodes. In previous EFG formulations, a grid of cells was used to perform Gaussian quadrature over the domain. The absence of a cell structure for nodal integration results in a completely meshless method, similar in simplicity to particle methods such as smooth particle hydrodynamics (SPH). It is shown that nodal integration, like SPH, suffers from spurious singular modes. This spatial instability results from underintegration of the weak form, and it is treated by the addition to the potential energy functional of a stabilization term which contains the square of the residual of the equilibrium equation. Example problems illustrate the effect of the stabilization and provide the basis for convergence studies.