STUDY ON NUMERICAL MANIFOLD METHOD BASED ON FINITE DEFORMATION THEORY

The large deformation of structure calculated by original numerical manifold method (NMM) is cumulated by small deformation calculated in each time step. However, when the structure undergoes large deformation and large rotation, the calculation strategy used in original NMM will lead to calculation error. In order to solve this problem, in this study, combining the interpolation function of NMM, the Numerical Manifold Method based on finite deformation theory is deduced from integral weak form of the momentum conservation equation and the stress boundary conditions. The comparison between the iteration schemes of original NMM and improved NMM points out the sources of error calculated by original NMM for the large deformation problem. Finally, examples of large deformation cantilever and rotation block are employed to exam the improved NMM. The numerical result shows that the improved NMM handles the problem involving in large deformation and large rotation very well. The result calculated by the improved NMM eliminates the errors caused by rotation of structure and is coincide with the analytical solution and Abaqus numerical solution very well.