Review and perspectives in applied mechanics of axially moving flexible structures

Abstract

This comprehensive review primarily concerns axially moving flexible structures in problems involving distributed structure-to-solid contact. The distinguishing features of axially moving structures are presented in terms of prevalent studies regarding models with simplified support conditions. Subsequent sections focus on the particular difficulties of treating contact problems with classical structural theories, on the appropriate non-material kinematic description for travelling structures, on the proper formulation of established mechanical principles for open systems and on the category of Arbitrary Lagrangian–Eulerian (ALE) approaches, which are frequently applied for the development of application-oriented finite element schemes. Novel analytical and numerical transient solutions for the benchmark problem of an axially moving beam, which is travelling across a rough surface between two misaligned joints, are presented to illustrate particular challenges as well as to highlight perspectives for future research activities. There are 177 references cited in this paper.

Determining the shape of a flexible thread in the field of horizontal and vertical forces

“…In [3], a comprehensive review of axially moving flexible structures in problems involving distributed contact of the structure with a solid body is given. The outlined features apply only to axially moving structures based on models with simplified support conditions.…”

Flutter instability in solids and structures, with a view on biomechanics and metamaterials

“…The recently published book by Banichuk et al. [61] is devoted to the stability analysis of initially straight and axially moving structures [62] such as strings, beams, plates or membranes. The structures are studied in terms of modal analysis, transverse vibrations, or stability and buckling, with application for instance to paper production.…”

“…Dynamic instabilities in axially moving structures of time-varying length are encountered in numerous technical applications, such as wire drawing, plastic extrusion, industrial robots, sheet paper printing, hoist and elevator systems [62], and deployment and retrieval of space tether systems [65], including solar sails [55,[66][67][68]. Elastic rods of varying length may be subject to configurational forces [69], which may concur with follower forces to create complex structural behaviours.…”

Divergence instabilities of nonuniformly prestressed travelling webs

“…For the past three decades there has been a significant growing interest in axially moving plate-like systems -a detailed assessment of this vast body of literature is beyond the scope of our present study. We refer to the recent comprehensive reviews [22,23,24,25], which give a good picture of the status quo in this area. The recent books [10,26] are also welcome additions to the literature, and should be consulted for more specialised accounts of past and present research.…”