Large Displacement Analysis of Tapered Beam Structures

A Bernoukki-Euler beam mechanism far static analysis of large displacement, large rotation but small strain planar tapered beam structures is proposed using the Updated Lagrangian formulation and the moving coordinate method. The object beam is the tapered one whose profile is assumed to be varying linearly. From the governing differential equation of lateral deflection including second-order effects by beam-column theory, the geometric nonlinear tangent elemental stiffness matrix is derived. The nonlinear effect of the bending distortions on the axial action is considered to manifest itself as an axial change in length. The aforementioned stiffness matrix is amended, by developing the auxiliary stiffness of bowing effect. The moving coordinate method is employed far obtaining the large displacement total equilibrium equations, and the hingedhinged moving coordinate system is constructed at the last updated configuration. The multiple load steps Newton-Raphson iteration is adopted far the solution of the nonlinear equations. The validity and effcidency of the proposed method are shown by solving various typical numerical examples.