| Summary: | 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.
|
|---|
