A finite element model for the vibration of spatial rods under various applied loads

Abstract In this study, a comprehensive energy formulation is outlined for the vibration analysis of spatially curved and twisted rods under various applied loads. In addition to the initial axial force, this formulation takes into account the initial moments and shear forces as well as initial deformations. The latter is accomplished through the updating of the curvature and twist of the rod under increasing loads. Based on this formulation, a spatially curved and twisted rod finite element is developed and used for analysis of several examples. The accuracy of the results obtained indicates that a small number of such elements can yield satisfactory results.