Straight configurations of shearable nonlinearly elastic rods
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Submission date: 21. Mar. 1998
published in: SIAM journal on applied mathematics, 60 (2000) 3, p. 1017-1036 (electronic)
In contact problems for elastic rods sometimes we have to look for a solution with some prescribed shape, in particular where some material curve has to be straight. While this question is a triviality for the Euler rod (or simplifications of it), the problem becomes much more subtle within the Cosserat theory which describes planar deformations of nonlinearly elastic rods that can bend, strech, and shear. For some selected material curve of the rod we assume that it is enforced to be straight by suitable external forces orthogonal to that straight axis. It is shown that such configurations satisfy a second order system of ordinary differential equations. In the case where this system is homogeneous a very rich structure can be observed by phase plane analysis. Finally some applications for rods which are in contact with a straight obstacle are discussed, and interesting new effects can be derived.