A New Algorithm in Computational Plasticity

• Main Authors: Chir Yuan Chen, 陳祺源
• Other Authors: Mr. Lei,Hin Chi
• Format: Others
• Language: zh-TW
• Published: 1994
• Online Access: http://ndltd.ncl.edu.tw/handle/70882150322064422962

碩士 === 國立中央大學 === 土木工程研究所 === 82 === Finite element method is usually used in analyzing engineering problems of elastoplastic solids. One of the major steps in solving the problems is to solve a nonlinear system of algebraic equations,which is a time-consuming iteration process. So far the most widely used iteration method is the Newton- Raphson method. Even though the Newton-Raphson method is superior in the speed of convergence to other existing iteration methods ,an elastoplastic problem solved by the method still takes a remarkable length of time.In this thesis a new iteration method is proposed which is found to have merits when compared with the Newton-Raphson method.In addition to elastoplastic problems, the new method can also be applied to solve nonlinear problems in soil consolidation,heat transfer,etc.. The features of the new method are as follows: 1.)it is better then the Newton-Raphson method in computational time and iteration number, 2.)when improving the degree of precision of the calculation one does not need to reform the stiffness matrix and re-solve for the inverse stiffness matrix if the new method is adopted, 3.)exact solution can be reached in one single step if one takes enough higher order terms into account when using the new method ,and thus the complicated step of evaluating the residual force is bypassed.