Application And Study Of Numerical Manifold Method In Geotechnical Engineering

Numerical manifold method is used for calculating the displacement and the deformation of the structure or the material, and it is capable of uniformly dealing with the problem of continuous deformation and discontinuous deformation. It has higher calculation precision for problem and is pop method of research for the numerical method in geotechnical engineering.Aiming at the theory and application of numerical manifold method, and combining the previous research work, this dissertation have researched the theory and application of numerical manifold method. The main works and research findings are written as following :(1) Have research the effects of cover displacement function to the stiffness matrix, put forward that x, y of basic progression functions has changed from the absolute value of coordinate in material region to opposite value of center coordinate in manifold element for amending the local character of the stiffness matrix in favor of solution, propose that the correct original coordinate is chose to exert the contribution of all order in the stiffness matrix and the stress matrix of equilibrium equations for increasing of precision in calculation.(2) Establish the modified functional of the analysis of the beam element and plate element, base on the generalized variational principle and penalty function method. Then, it is used to create the beam and plate manifold element and the format of manifold element( such as displacement function, strain matrix and stiffness matrix etc).(3) Aim at the bending problem of the moderately thick plate, the numerical manifold method of the Mindlin plate on the Winkler foundation is put forward, based on the principle of the numerical manifold method. It is significative to some bending problem of the moderately thick plate on the elastic foundation in engineering analysis.(4) Do some tentative analysis of the tunnel lining by numerical manifold method. the idea is given that combining regular mesh with finite element mesh and using low-order and high-order cover displacement function in numerical manifold method, it make preprocess and program analysis, precision and efficiency for coordination.(5) Give the numerical manifold method for nonlinear analysis by researching the consitistutive models used in numerical manifold method presently. Nonlinear models(Duncan-Chang model and K-G model )are used in this paper, and useful numerical analytic method is provided for nonlinear analysis of numerical manifold method in geotechnical engineering.(6) Construct the three-dimensional manifold element covering hexahedron, provide cover displacement function, strain matrix, stiffness matrix and stress matrix of the three-dimensional manifold element by the previous research work. With the example computation analysis and comparison with analytical solution and ANSYS computation result, the method is proved to be effective.(7) Programmed the Object-Oriented program with C++ language in VC++ platform. It is capable for calculating the common problem of manifold method (such as these correlative problems in the paper etc), and has better preprocess and postprocess function. The program is proved to be effictive and feasible by example.