Abstract. We give a careful discussion of end rotation in elastic rods, focusing on ambiguities that arise if arbitrarily large deformations are allowed. By introducing a closure and restricting to a class of deformations we show that a rigorous treatment of end rotation can be obtained. The results underpin various non-rigorous discussions in the literature and serve to promote the variational analysis of boundary-value problems for rods undergoing large deformations. As an example we discuss the application to the model of a rod lying on the surface of a cylinder.
C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a MAS Modelling, Analysis and Simulation Modelling, Analysis and SimulationSelf-contact for rods on cylinders G.H.M. van der Heijden, M.A. Peletier, R. Planqué Self-contact for rods on cylinders ABSTRACT 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 ode 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. Abstract. 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. REPORT MAS-E0411 AUGUST 2004Using techniques from ode 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 selfcontact points is continuous, a result that contrasts with known examples from contact problems in free rods.
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