A hierarchical non-intrusive algorithm for the generalized finite element method

Abstract

Abstract An algorithm for non-intrusively coupling a commercial finite element software with a research code implementing a hierarchical enrichment of finite element spaces is presented. Examples of hierarchical methods supported by the algorithm are the Generalized or eXtended FEM (GFEM), the scale-bridging GFEM with numerically defined enrichment functions (GFEM$$^\text {gl}$$ gl ), and the p-version of the FEM. The proposed hierarchical non-intrusive algorithm (HNA) combines the vast library of classical elements available in commercial FEM platforms with the ability of the GFEM$$^\text {gl}$$ gl to analyze localized phenomena like cracks and spot welds, on coarse meshes. The algorithm does not require iterations between the standard and Generalized FEM platforms and is simple to implement. Examples showing the application of the HNA to the coupling of Abaqus with a 3-D GFEM$$^\text {gl}$$ gl software are presented. They also demonstrate the benefits of combining finite elements available only in a commercial platform with a GFEM.

Keywords

• Finite element method
• Generalized FEM
• GFEM
• eXtended FEM
• XFEM
• Non-intrusive