弧長法による弾性座屈問題の解析 : (その 2) 数値解析方法としての弧長法

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This is the second of two successive papers. In the previous paper, the nature of first-order incremental solution at buckling point was studied. The purpose of this paper is to propose new numerical method of equilibrium path before and after buckling. The contents are as follows. 1) Introduction 2) Ordinary incremental method 3) Calculation of fundamental path by arc length method 4) Calculation of bifurcate path by arc length method 5) Numerical examples 6) Conclusion The arc length method, which uses the arc length of equilibrium path as an incremental parameter, is originally the numerical method for fundamental path. Now, it is extended for bifurcate analysis. The features of arc length method applied to the bifurcate analysis are, (1) for the purpose of obtaining homogeneous mode {α} (namely, eigen mode with zero eigen value) and paticular mode {β}, we need not calculate the eigen value of [K], but have only to calculate the inverse of [K]. (2) in case of deciding unknow parameter c and p, which are contained in the expression c{α}+p{β}, we calculate them in the Newton-Raphson convergency process, by trial and error. That is to say, by the arc length method, we need not caluclate the second-order incremental equation which is used by the static perturbation method, as well as the eigen value problem. By numerical examples of bifurcate analysis, the arc length method shows good convergency.
1976-05-30