MULTIPLE 3-DIMENSIONAL EQUILIBRIUM SOLUTIONS FOR CANTILEVER BEAMS LOADED BY DEAD TIP AND UNIFORM DISTRIBUTED LOADS

The development of multiple solutions for orthotropic cantilever beams in a fully three-dimensional setting is investigated. The governing e quations are solved using an iterative shooting procedure that convert s the original boundary value problem into a sequence of initial value problems that converge to the desired solution. This method is well s uited to finding multiple equilibrium solutions. Several classes of eq uilibrium configurations are described and illustrated including plana r shapes, buckled planar shapes and fully three-dimensional configurat ions which appear far removed from the initial plane of loading. The s olutions for the planar shapes and the buckled configurations compare favourably to previously published results. The development of the far -removed shapes is shown to be qualitatively similar to that of the pl anar shapes. The behaviour is shown to be highly dependant upon the as pect ratio of the cross-section. For certain aspect ratios it is shown , somewhat surprisingly, that out-of-plane equilibrium solutions can e xist at loads below those required for multiple planar solutions. (C) 1996 Elsevier Science Ltd.