Application of Differential Transformation Method and Dunkerley Formula for Stability Analysis of Bars in Water

Abstract

In this study, two methods have been proposed to find the critical buckling load of bars that arein water and buckled under the effect of P singular force and distributed self-weight. Threedifferent Euler's cases were taken into account in the study. In the first method, the solution ofthe stability differential equation of the bar in water is solved by the Differential TransformationMethod (DTM), while in the second method, the Dunkerley formula is applied to determine thecritical buckling load factor of the buckled bar in water. Finally, the results obtained by solvingan example with the two proposed methods were compared with the finite element method. SAP2000 program was used for finite element analysis. From the results obtained, it was observedthat the two methods gave results in good agreement to the finite element method.