ON THE USE OF A SEGMENTAL SHOOTING TECHNIQUE FOR MULTIPLE SOLUTIONS OF PLANAR ELASTICA PROBLEMS

The solution of the non-linear equation of equilibrium for plane elast ica problems is avoided by using a segmental shooting technique. In th is 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 compatibi lity 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 b oundary conditions using a shooting technique. Since only one segment is considered at a time, the numerical calculations can be done accura tely and efficiently on a PC type computer. When multiple solutions ex ist, the procedure outlined is useful in determining all of the soluti ons 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.