MULTIPLE SOLUTIONS FOR INEXTENSIBLE ARCHES

The multiple equilibrium solutions of both deep and shallow inextensib le arches is investigated through the use of a segmental shooting tech nique. The original nonlinear boundary value problem governing the lar ge deformations of these arches is solved using a sequence of linear i nitial value problems which converge iteratively to the required bound ary conditions. This method has proved successful in previous studies to analyse these large deformation problems when there is initially on ly one unknown at the beginning of the arch that must be assumed. Exte nsion of this method to the problem with two initial unknowns is prese nted here. In either case all equilibrium solutions can be found in a systematic fashion. When there are three initial unkowns the present m ethod is not able to determine the totality of equilibrium shapes for a given problem and loading. However, in this case, it is possible to determine a number of equilibrium shapes using engineering judgement f or the values of the initial unknowns.