A Novel Solution for Seepage Problems Implemented in the Abaqus UEL Based on the Polygonal Scaled Boundary Finite Element Method

Abstract

The scaled boundary finite element method (SBFEM) is a semianalytical computational scheme based on the characteristics of the finite element method (FEM) and boundary element method that combines their respective advantages. In this paper, the SBFEM and polygonal mesh technique are integrated into a new approach to solve steady-state and transient seepage problems. The proposed method is implemented in Abaqus employing a user-defined element (UEL). A detailed implementation of the procedure is presented in which the UEL element is defined, the internal variables RHS and AMATRX are updated, and the stiffness/mass matrix is solved using eigenvalue decomposition. Several benchmark problems are solved to verify the proposed implementation. The results show that the polygonal element of the polygonal SBFEM (PSBFEM) is more accurate than the standard FEM element of the same element size. For transient problems, the results for the PSBFEM and FEM are in excellent agreement. Hence, the proposed method is robust and accurate for solving steady-state and transient seepage problems. The developed UEL source code and the associated input files can be downloaded from GitHub.