In this manuscript, a new way of determining the buckling load of the two-stage both end-hinged, single acting hydraulic cylinder has been engrossed using successive approximation method. The method has been extended from single stage hydraulic cylinder to the two-stage hydraulic cylinder mounted with pin support at both ends. This method includes a few numbers of iterations required in order to achieve good accuracy or in other words getting the minimum error. Further, finite element analysis of the hydraulic cylinder has also been performed for the validation purpose. The buckling mode shape for three different modes and their corresponding buckling load has also been obtained using the finite element method. The approximation of the buckling load corresponding to the first buckling mode shape has been performed and observed load lies in the close vicinity of theoretical calculation. The critical load obtained using a successive approximation method after two iteration shows the minor deviation of 3.63%.

中文翻译：

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伸缩筒屈曲载荷的逐次逼近法

在此手稿中，采用了逐次逼近法，提出了一种确定两级两端铰接单作用液压缸屈曲载荷的新方法。该方法已从单级液压缸扩展到在两端都装有销支撑的两级液压缸。该方法包括一些迭代，以实现良好的精度，或者换句话说，获得最小的误差。此外，还出于验证目的对液压缸进行了有限元分析。还使用有限元方法获得了三种不同模式的屈曲模式形状及其对应的屈曲载荷。已经执行了与第一屈曲模式形状相对应的屈曲载荷的近似计算，并且观察到的载荷接近理论计算值。在两次迭代之后，使用逐次逼近法获得的临界载荷显示出3.63％的较小偏差。