2017 年 83 巻 854 号 p. 17-00300
In this paper, formulations and some computational results of cycle jump method based on the nonlinear finite element method are presented. Problems, involving nonlinear cyclic deformation, such as low cycle fatigue problems can be solved by the proposed cycle jump method. To solve the problems of nonlinear cyclic deformation of structure by the nonlinear finite element method with a cycle-by-cycle approach, a large amount of computational time is generally required. Thus a cycle jump method is presented from a view point of temporal multi-scale analysis. Then, an alternative analytical procedure consisting of three steps is proposed. They are a few cycles of nonlinear analysis in a cycle-by-cycle fashion, computations of jumps of strain history dependent quantities (extrapolations) based on the results of the cycle-by-cycle analysis and a cycle jump for several dozen to several hundred cycles using the results of the extrapolations. The results of cycle jump analyses are presented and their accuracies are critically examined. It was found that the results of several load cycles at the beginning of each cycle-by-cycle analysis step should be excluded from the computations of the extrapolation step.