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The Generalized Finite Element Method (GFEM) presented in this paper combines and extends the best features of the finite element method with the help of meshless formulations based on the Partition of Unity Method. Although an input finite element mesh is used by the proposed method, the requirements on the quality of this mesh are significantly relaxed.(More)
SUMMARY A general GFEM/XFEM formulation is presented to solve two-dimensional problems characterized by C 0 continuity with gradient jumps along discrete lines, such as those found in the thermal and structural analysis of heterogeneous materials or in line load problems in homogeneous media. The new enrichment functions presented in this paper allow(More)
This paper describes extensions of the hp cloud method to problems of fracture mechanics as an example of developing customized cloud functions. The cloud methods are built on partitions of unity that are subordinate to covers of the solution domain. For this reason, clouds can also be constructed on nite element meshes. This aspect of these methods is also(More)
A mapping method is developed to integrate weak singularities which result from enrichment functions in the generalized/extended FEM. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D(More)
A new methodology to build discrete models of boundary-value problems is presented. The h-pcloud method is applicable to arbitrary domains and employs only a scattered set of nodes to build approximate solutions to BVPs. This new method uses radial basis functions of varying size of supports and with polynomial-reproducing properties of arbitrary order. The(More)
The present paper summarizes the generalized ®nite element method formulation and demonstrates some of its advantages over traditional ®nite element methods to solve complex, three-dimensional (3D) structural mechanics problems. The structure of the sti€ness matrix in the GFEM is compared to the corresponding FEM matrix. The performance of the GFEM and FEM(More)