The scaled boundary finite element method (SBFEM) is an alternative method to construct polygonal elements. Therefore, these advantages have further motivated polygonal elements as an alternative to conventional FEM using triangles or quadrilaterals. Moreover, it is more flexible in the discretization of complex geometry. Simultaneously, they generally exhibit superior solution accuracy. Polygonal element with more than four sides involves more nodes in their interpolation compared with a conventional FEM. To overcome the weakness above the conventional FEM, researchers proposed other alternatives methods, such as the meshfree method, the smoothed finite element method, the Isogeometric Analysis (IGA), Deep Neural Networks (DNNs), and the polygonal finite element method. These elements used in conventional FEM must conform to the domain’s boundary, which leads to difficulty in solving many complex problems. For example, (a) the accuracy of the solution depends on the quality of the mesh and (b) requires sophisticated discretization techniques to generate high-quality meshes and to capture topological changes. At present, the conventional FEM also faces several problems. Typically, the shape of the conventional two-dimensional finite element method is triangles or quadrilaterals. A domain of complex geometry is partitioned into a finite number of nonoverlapping subdomains of simplex shapes by introducing the concept of discretization. The finite element method (FEM) is a reliable computational tool to solve partial differential equations (PDE) in science and engineering. The developed UEL and the associated input files can be downloaded from. The implementation of PSBFEM-UEL can conveniently use arbitrary polygon elements by the polygon/quadtree discretizations in the Abaqus. The results show that PSBFEM-UEL has significantly better than FEM convergence and accuracy rate with mesh refinement. Several benchmark problems from two-dimensional linear elastostatics are solved to validate the proposed implementation. Moreover, we also develop the preprocessing module and the postprocessing module using the Python script to generate meshes automatically and visualize results. The details on the main procedures to interact with Abaqus, defining the UEL element, and solving the stiffness matrix by the eigenvalue decomposition are present. The PSBFEM is implemented by the User Element Subroutine (UEL) feature of the software.
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This work discusses developing a PSBFEM framework within the commercial finite element software Abaqus. The polygonal scaled boundary finite element method (PSBFEM) is a novel method integrating the standard scaled boundary finite element method (SBFEM) and the polygonal mesh technique.