A Study on the Efficient and Robust Numerical Method for Nonliner Equilibrium Equation

Eiji IWASAKI Masatugu NAGAI

In nonlinear analysis, it is thought that the nonlinear analysis system which reduces an indefinite parameter physically and input data can create easily needs to be developed required for convergency or a solution. Then, in the arc length controlling method, this study investigates about a setting method of a scaling parameter that defines the arc length that decided by trial and error, moreover, expand the arc length automatic setting-up method that was corresponding to only a primary path so that it is able to correspond to a secondry path and confirmed these compatibility and efficacy. As a result, by the example of numerical computation, the following conclusions were obtained.

By the setting method of a scaling parameter by this research, the scaling parameter on the load define a constant, the controlling parameter by the scaling parameter on the displacement define the all displacement component, by checking the equilibrium curve by the all translational displacement components and the load factor, the proper scaling parameter is able to set, decision of the scaling parameter becomes easier than the conventional method and decrease trial and error.

The arc length automatic setting-up method devised by past reseach adjust to only the primary path, but extend such that it is able to calculate to the secondry path by this reseach, the move from the primary path to the secondry path is smoothly and the secondry path is able to calculate that become stable.

Therefore, the efficacy and robustness of this study was able to confirm.