Mg. Faulkner et al., ON THE USE OF A SEGMENTAL SHOOTING TECHNIQUE FOR MULTIPLE SOLUTIONS OF PLANAR ELASTICA PROBLEMS, Computer methods in applied mechanics and engineering, 110(3-4), 1993, pp. 221-236
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.