The numerical algorithms for elastoplastic models under mixed control

• Main Authors: Chi-Fu Li, 李奇富
• Other Authors: Chein-Shan Liu
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/68961156878955506893

碩士 === 國立臺灣海洋大學 === 機械與輪機工程學系 === 92 === In this paper we attempt to use group preserving scheme (GPS) in five-dimensional space to search numerical solution of the Armstrong-Frederick kinematic hardening model with back stress, and employ the mixed-controlled idea to re-constitute the Prager kinematic hardening model by hoping to reach the result that the traditional strain or stress control can not be applied. Furthermore, we make the model more complicated with material function being employed and discuss briefly the mixed-control model failure, and compare it to the original model to get more useful information. In this thesis we first convert the nonlinear dynamical system,into an augmented dynamical system of Lie type ,locally. In doing so, the inherent symmetry group and the (null) cone structure of nonlinear dynamical system are brought out; then the Cayley transformation and the exponential transformation are utilized to develop group preserving schemes in the augmented space. The schemes are capable of updating the augmented state point to locate automatically on the cone at the end of each time increment. By projection we thus obtain the numerical schemes on state space , which have the form similar to the Euler scheme but with the weighting factor being adaptive. The classic radial return method (RRM) is employed to compare with group preserving scheme, which ascertains the accuracy and efficiency of the latter scheme. A good scheme should be accurate both in stress magnitude and in stress orientation. The relative errors in strain and stress are employed to assess the stress magnitude, and the isoerror maps are employed to check the stress orientation. A series of compassions and Figures are utilized to assess the accuracy and efficiency of our algorithms.