Analytic solutions for nonlinear differential equations describing the elastica of straight bars: Theory. (English) Zbl 0655.73028
It is well known that the classical elastica problem under end forces is integrable with elliptic functions. The authors show that also for more general types of loading, that is, in addition to forces also couples are acting at the ends of the rod and also uniformly distributed forces along the axis of the rod are allowed, a closed form analytic solution in form of elliptic functions can be found. This remarkable result is achieved by applying certain functional transformations.
Reviewer: H.Troger
MSC:
| 74G60 | Bifurcation and buckling |
| 74B20 | Nonlinear elasticity |
| 74K10 | Rods (beams, columns, shafts, arches, rings, etc.) |
| 33E05 | Elliptic functions and integrals |
Keywords:
end couples; closed form integration of exact differential equation; compression; bending; uniformly distributed forces; closed form analytic solution; elliptic functions; functional transformationsReferences:
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