Deformation of a spatial elastica constrained inside a springy tube
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Most previous works on spatial elastica constrained inside a tube assumed that the tube wall is rigid. This assumption is not adequate when it involves human artery and tissue. In this paper, we study the deformation of a clamped–clamped rod constrained within a straight flexible tube. The reactive force exerted on the rod is assumed to be only in the radial direction and proportional to the radial displacement of the tube wall at the contact point. The results are compared with those of a rigid tube. The complicated deformations, which change from contact to non-contact within a tight range, can exist only when the tube is rigid. As the tube becomes more flexible, the dramatic variation of contact and non-contact tends to be eased off. It is shown that the peculiar phenomenon of concentrated force pairs on the edges of line-contact segment in the rigid tube model can be captured by the springy wall model as the spring constant approaches infinity. It is also found that the maximum lateral protrusion of the flexible tube does not necessarily occur at the midpoint of the rod.
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