Numerical Manifold Method
Introduction to Numerical Manifold MethodAiming global analysis, the well known mathematical manifold is perhaps the most important subject of modern mathematics. Based upon mathematical manifold, this numerical manifold method is a newly developed general numerical method. This method computes the movements and deformations of structures or materials. The meshes of the numerical manifold method are finite covers. As the material domains, the finite covers overlapped each other and covered the entire material volume. On each cover, the manifold method defines a independent cover displacement function. The cover displacement functions on individual covers are connect together to form a global displacement function on the entire material volume.
The global displacement function are the weighted averages of local independent cover functions on the common part of several covers. Using the finite cover systems, continuous, jointed or blocky materials can be computed in a mathematically consistent manner. For a manifold computation, the mathematical covers and physical mesh are independent. Therefore, the mathematical covers is free to define and free to change. The mathematical covers can be moved, can be split and can be easily removed and added. Moving the covers, the large deformations and moving boundaries can be computed by steps. The joints, block boundaries can divide a cover to two or more independent covers together with their displacement functions, then the general discontinuous materials can be modeled.
Both the finite element method (FEM) for continua and the discontinuous deformation analysis (DDA) for block systems are special cases of this numerical manifold method. In the current development stage of numerical manifold method, by using finite cover approach, the extended finite element method can compute more flexible and visible deformations and movements of joints and blocks.
Source DownloadThe original version of 2D NMM written by Dr. Shi is distributed under MIT license. Follow these links to get the software:
Source codes for Windows 32bit