A View on Manifold Method Comparing with Fintite Element Method

Numerical modeling problems can be categorized into two types: continuous deformation analysis and discontinuous deformation analysis in most cases. The former is mainly concentrated on strain-stress analysis for continuous media with small deformation. Finite Element Method (FEM) is one of the well-known methods widely used for this purpose. The latter is mainly concentrated on simulating failure propagation, rigid body movements of discontinuous media with large deformation. Distinct Element Method (DEM) (Cundall. 1980) and Discontinuous Deformation Analysis (DDA) (Shi & Goodman, 1984) are known as the effective methods for this kind of simulations. However, as the development of computation technology, it is a strong requirement that a numerical analysis method should be applicable to both the continuous and discontinuous analysis for solving the same problem. For this reason, the Manifold Method (MM) (Shi, 1991) is attracting attentions of geotechnical engineers more and more because it is just the method applicable to both continuous and discontinuous analysis. MM was developed by Shi in 1991 and further improved in 1997. It contains and combines FEM and DDA in a unified form. In handling discontinuities such as faults, joints and cracks, MM takes over all the advantages of DDA, and for strain-stress analysis problems, it is as powerful as FEM. Therefore, MM can be considered as a potential effective numerical method for geotechnical modeling. In order to pursue its practical applications in geotechnical engineering, the theory of MM has been introduced by means of approximation theory instead of the original topological concepts in this paper. Close comparisons of MM with FEM based on triangular mesh have been made in various aspects such as formulization procedures, definitions of elements and displacement functions, integration methods. Thus, the correspondences and differences between MM and FEM have been outlined, and the merits of MM over FEM have also been summarized clearly. And these merits have been shown by two application examples. Therefore, we expect that the Manifold Method will be put into wide applications in civil engineering