The Analysis And Application Of The Rigid-plastic Numerical Manifold Method

In order to study the states of strain and stress which excess the bending point after the linear elasticity, specially the big distortion which be often met during the manufacture, the elastic and plastic finite element method and the rigid-plastic finite element method occurs successively. But, when dealing with the big distortion, the elastic and plastic finite clement method needs the very small increment of the time, wastes much time of calculating and CPU, at the same time, the calculating tolerance will be very much; at the occasion where the elastic distortion can be neglected, although the rigid-plastic finite element method can resolve the problem of the calculating tolerance by computing the stress directly during every time step, it has to depend on the abundant data of grids to enhance the precision of calculation.The modern Numerical Manifold Method(NMM) is a new method of numerical value with general meaning. What is different from the traditonal finite element method which only has the single covering is that the NMM adopt two sets of separate grids of maths grid and physies grid,Thereinto, the maths grid defines the precision of calculation, which can avoid the problem that needs to add the data of grid for enhancing the precision, Further more, NMM also can resolve the problem of discontinuous distortion, NMM unifies the finite element method and the discontinuous distortion analysis. Due to the many merits of NMM, NMM has been paid more and more attention.In the dissertation, basing on the merits and the defects of the traditional rigid-plastic finite element method, the academic system and the calculating formulas have been established by importing the NMM to the rigid-plastic finite element method. Considering the extensive application of the isoparametric quadrangle, the formulas of rigid-plastic finite element method with the isoparametric quadrangle are emphasized to deduce,...