Three-dimensional partition-of-unity generalized node method for the simulation of fractured rock mass

A three-dimensional (3D) partition-of-unity (PU) generalized node method (GNM) is developed for the simulation of fractured rock mass. In the 3D PUGNM, generalized nodes with independent deformations are directly defined on the isolated blocks to simplify the construction of PU approximations in 3D problems. The explicitly representing of polyhedral blocks with complex geometric shapes by a proper topological structure, the computational geometric algorithms for block cutting, and the subdivision of integration tetrahedrons adapting to physical boundaries are totally avoided in the present 3D PUGNM, and thus the bottleneck problems encountered in the existing PU methods for three dimensions have been well solved. The present 3D PUGNM has the advantages of simple data structure, strong robustness, and convenient numerical implementation, and paves the way for promising application in various engineering problems. Several numerical examples are tested to demonstrate the accuracy, correctness and robustness of the proposed method.