摘要
本文针对理想弹塑性材料,对目前适用于非线性有限元计算的多种增量迭代法进行比较研究。增量方式分位移增量和荷载增量两种,迭代方式分广义Newton-Raphson法、修正Newton-Raphson法和初始刚度法三种。研究表明:对理想弹塑性材料,荷载增量迭代法的计算结果,或明显不合理,或误差较大,或出现计算不稳定。位移增量迭代法中,初始刚度法计算结果最为理想,但在迭代次数较多的情况下,有可能出现"误差敏感性",宜引入加速收敛的技术。
In this paper, some incremental iterative methods used in the nonlinear FEM computation for the ideal elastoplastic materials are studied and compared each other. Increments can be divided into displacement one and load one. Iterative manner can be divided into general Newton - Raphsoni one and revised Newton - Raphsoni one and initial matrix one. The research results show that for the ideal elastoplastic materials applying load increment iterative method in the computation the results obtained are obviously unreasonable or the computation errors are bigger or the computation results are unstable. Among the displacement incremental iterative methods, the computation results of initial matrix method are idealest, but in the case of needing many iterative times, error sensitivity may produce, and the technique to accelerate the computation convergence should be introduced.
