A twisted elastica constrained inside a tube

• The two ends of the rod are clamped at the center of tube cross section.
• Free of contact, point contact, and line contact may develop in the deformation.
• The results from elastica model and small-deformation theory are compared.
• Small-deformation theory can predict only the early stage of deformation.
• Elastica model predicts that snapping jump and self-contact will occur.

In this paper we use elastica model to calculate the deformation of a clamped–clamped rod under end twist and constrained inside a straight tube. Unlike most of the previous works, in which only the fully-developed line-contact spiral from end to end was considered, we study the case when both ends of the rod are at the center of the tube cross section. As a consequence, free of contact and point contact may occur in the deformation. The results are compared with those predicted from a previous work using small-deformation theory. Ten deformation patterns from deformation 1–10 are calculated by shooting method, with a possibility of finding more. The deformation sequence forms a smooth load-deflection locus. It is found that the small-deformation theory is capable of finding only the early stage of the deformation sequence from deformation 1 to 5. The elastica model, on the other hand, predicts that the constrained elastica may undergo snapping jump and self-contact when it is under load or displacement control. These deformations cannot be found from a small-deformation theory.