An enhanced octree polyhedral scaled boundary finite element method and its applications in structure analysis

In this paper, an enhanced octree polyhedral scaled boundary finite element method (SBFEM) is proposed in which arbitrary convex polygon (pentagon, hexagon, heptagon, octagon etc.) can be directly served as boundary face elements. The presented method overcomes the existing SBFEM's limitation that boundary face is strictly restricted to be a quadrangle or triangle. The conforming shape functions are constructed using a polygon mean-value interpolation scheme for polyhedral face. A highly efficient octree mesh generation technology is introduced to accelerate the progress of pre-treatment, wherein the mesh information can be directly used in the enhanced SBFEM. The accuracy of the proposed method is first verified using a beam under shear and torsion load. Another three more complicated geometries including a nuclear power plant structure, as well as two sculptures named Terra-Cotta Warriors and Sioux Falls Church are presented to demonstrate the application and robustness of the proposed method. The new method possesses appealing versatility and offers a swift adaptive capacity in mesh generation, which can provide a powerful technique for the simulation of complex geometries, rapid-design analysis and multi-scale problems.