On the use of a segmental shooting technique for multiple solutions of planar elastica problems

Abstract The solution of the non-linear equation of equilibrium for plane elastica problems is avoided by using a segmental shooting technique. In this procedure, the rod is divided into a series of segments, with each one undergoing only small deformations. The segments can be loaded in various manners and solved individually. Geometric and force compatibility is used to assemble the segments to allow analysis of the entire rod. The original boundary value problem is then solved by considering a sequence of initial value problems which converge to the required boundary conditions using a shooting technique. Since only one segment is considered at a time, the numerical calculations can be done accurately and efficiently on a PC type computer. When multiple solutions exist, the procedure outlined is useful in determining all of the solutions and in giving a partial understanding of the stability of each of the particular solutions. The procedure is applied to cantilevers and semi-circular arches to illustrate the technique.