Hybrid Method of Polygonal and Quadrilateral Elements for Modeling Jointed Rock Mass

Abstract

In the numerical simulation of heterogeneous materials, such as jointed rock mass, it is extremely difficult to perform meshing for constricted regions, resulting in time-consuming modeling and inaccurate computations. To this end, this paper presents a hybrid method of polygonal and quadrilateral elements based on the finite element method. The function of barycentric rational interpolation from the mean value principle is introduced and the shape function of the polygonal element is established. The polygonal element can be directly used for meshing constricted regions of the heterogeneous material. Moreover, it avoids the singular matrix and time-consuming meshing due to the particular geometry of this region. The coupling process of the polygonal element and quadrilateral element is demonstrated. The proposed hybrid method was implemented in several benchmarks examples to demonstrate its accuracy and capabilities. Quantitative comparisons of the numerical method and analytical solutions showed good approximation. The proposed hybrid method has advantages of improved preprocessing efficiency, simple implementation, high accuracy, and robustness compared with the conventional finite element method. In addition, this method is significant for the numerical modeling of complex geometries and provides a better solution for heterogeneous materials in engineering practice.