On the use of a segmental shooting technique for multiple solutions of planar elastica problems. (English) Zbl 0847.73073
The solution of the nonlinear 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 the shooting technique. The procedure is applied to cantilevers and semi-circular arches to illustrate the technique.
MSC:
| 74S30 | Other numerical methods in solid mechanics (MSC2010) |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
Keywords:
convergence; boundary value problem; sequence of initial value problems; cantilevers; semi-circular archesReferences:
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