An ABAQUS Implementation of the Cell-Based Smoothed Finite Element Method (CS-FEM)

The smoothed finite element method (S-FEM) has been developed recent years and is increasingly used for stress analysis for engineering design of structures, due to its high computational accuracy and outstanding robustness in against mesh distortion. However, there is currently no commercial S-FEM software package available for convenient engineering applications. This paper aims to integrate S-FEM into the ABAQUS (R) software, because it is most widely used in engineering analyses and well integrated in computer aided engineering (CAE). From a family of S-FEM models, the cell-based finite element, method (CS-FEM) is chosen to be implemented in ABAQUS, because a smoothing cell in the CS-FEM involves only one element, and hence the implementation can be achieved via the use of the user-defined element library (UEL). Since only nodal displacement results can be extracted when UEL subroutine is used in ABAQUS, a post-processing program is also developed to compute nodal strains/stresses and strain energy results that are useful in structure analysis and CAE. Our CS-FEM UEL is validated using four numerical examples under plane stress conditions. Compared with standard ABAQUS, the CS-FEM in ABAQUS improves the solution accuracy remarkably, and we have also confirmed the robustness of CS-FEM against heavily distorted meshes.