The Generalized Finite Element method on eight-node element meshes

Based on the PUM paradigm, this paper presents formulae of the Generalized Finite Element Method (GFEM for short) for static analysis, with Dirichlet boundary conditions imposed by Lagrange multipliers. On the traditional two-dimensional eight-node element meshes, the generalized shape functions and relative formulae are setup. Then it is more familiar to model complex problems exactly without fine meshing, as necessary with common FEM. Linear dependency of the discrete system is analyzed, and a simple but efficient method, partial enrichment, is suggested to reduce, even avoid linear dependency. With this approach, the scale of the system is also decreased substantially and the feature of high accuracy of the GFEM is maintained satisfactorily. Efficiency of different implementation methods is studied with an example of stress concentration, and the results show that the GFEM is superior to the conventional FEM in terms of efficiency, precision and cost. The GFEM is also proved effective for volume-locking problems.