2004/11/02 by G.H.M. van der Heijden, G. H. M. van der Heijden, M. A. Peletier +6
Computer Science · Engineering · Mathematics · Physics and Astronomy · #34C11 #34C25 #34C60 #47J30 #49J40 #74G25 #74G55 #74G65 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #Contact Mechanics and Variational Inequalities #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.CA #math.MP #msc:34C11 #msc:34C25 #msc:34C60 #msc:47J30 #msc:49J40 #msc:74G25 #msc:74G55 #msc:74G65
paper · pdf · doi:10.48550/arxiv.math-ph/0411007
42 pages, 11 figures
arxiv created 2004/11/02 · openalex publication_date 2004/11/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.