Self-Contact for Rods on Cylinders
- 147 Downloads
We study self-contact phenomena in elastic rods that are constrained to lie on a cylinder. By choosing a particular set of variables to describe the rod centerline the variational setting is made particularly simple: the strain energy is a second-order functional of a single scalar variable, and the self-contact constraint is written as an integral inequality.
Using techniques from ordinary differential equation theory (comparison principles) and variational calculus (cut-and-paste arguments) we fully characterize the structure of constrained minimizers. An important auxiliary result states that the set of self-contact points is continuous, a result that contrasts with known examples from contact problems in free rods.
- 1.Antman S.S.: Nonlinear problems of elasticity. Springer-Verlag, 1995Google Scholar
- 4.Cantarella, J., Fu, J.H.G., Kusner, R., Sullivan, J.M., Wrinkle ,N.C.: Criticality for the Gehring link problem. arXiv: math.DG/0402212, 2004Google Scholar
- 8.Doedel, E., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Sandstede, B., Wang, X.: Auto97: Continuation and bifurcation software for ordinary differential equations; available by ftp from ftp.cs.concordia.ca in directory pub/doedel/autoGoogle Scholar
- 10.Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order. Springer-Verlag, 1977Google Scholar
- 15.van der Heijden, G.H.M., Peletier, M.A., Planqué, R.: On end rotations for open rods undergoing large deformations. submitted to Arch. Ration. Mech. Anal. arXiv: math-ph/0310057, 2005Google Scholar
- 20.Protter, M.H., Weinberger, H.F.: Maximum principles in differential equations. Prentice-Hall, 1967Google Scholar