Three-dimensional MLS-based numerical manifold method for static and dynamic analysis

Due to its unique feature for both continuous and discontinuous problems, Numerical Manifold Method (NMM) has made great achievements in many fields in recent years; however, most of them focused on two dimensions. One of the major obstacles for three-dimensional (3D) NMM is the cover generation algorithm, which needs to implement 3D cutting algorithm to generate the physical cover (PC) and manifold elements. In this study, based on the previous 2D Moving Least Squares (MLS) based NMM, a 3D version (denoted as 3D MLS-based NMM) is proposed to bypass the complex preprocessing algorithm. By constructing the mathematical cover (MC) with the influence domains of MLS-nodes, intersection of MC and problem domain is avoided in the generation of the PC, which can significantly simplify the preprocessing. Meanwhile, a regular nodes arrangement can always be employed, which preserves the elegant feature of NMM and also leads to better accuracy. Apart from static problems, free and forced vibration problems, seldom touched by 3D NMM, are also analyzed. Several numerical examples are presented to validate the effectiveness and accuracy of the proposed method. The results show that 3D MLS-based NMM has high accuracy, continuous stress field and excellent convergence rate.