Large deflections of nonlinear elastic and viscoelastic columns with follower loads: the elastica and viscoelastica problems

Abstract

Large deflection analyses of nonhomogeneous nonlinear elastic or viscoelastic columns (elastica and viscoelastica) with initial curvature and with deflection dependent cross sectional areas subjected to follower loads are formulated. Column end shortening due to both curvature and compressive loads is taken into account and the governing coupled nonlinear dierential equations are solved by successive approximation methods (SAM) and numerically by a dou- ble Runge-Kutta iterative shooting approach. Various solution protocols are analyzed and evaluated. The eects of end shortening and follower load angle on elastic and viscoelastic columns are discussed. The hierarchal setting between column instability and material failures is examined.