Choice of the model in problems of contact between thin-walled bodies

Specific Features of the Contact Interaction and Wear of Thin-Walled Structural Elements

“…These problems become especially urgent in connection with the intense introduction of units with contact interaction of thin-walled structural elements into the contemporary engineering practice. In this case, contact problems differ from the classical contact problems of the theory of elasticity [6,8,41,43,54,62,65] and their solution requires the application of different mathematical methods [11,20,64,73,77,80,81]. By using different versions of the theory of plates and shells, one can significantly simplify the mathematical model of the problems of contact interaction and wear and, at the same time, take into account the anisotropy of physicomechanical and thermal characteristics of contacting bodies (typical of new modern antifriction composite materials) and the presence of thin protective coatings [9,47,61,70,71,75].…”

“…The extensive introduction of thin-walled structural elements, new composite materials, bodies with coatings, interface interlayers, patches, and stiffening ribs into engineering practice leads to the intense development of the investigations of contact problems for these structures. On the one hand, this class of contact problems is closely related to the classical contact problems of mechanics of deformable bodies and, on the other hand, it is characterized by certain specific features of the transfer of loads in the course of contact of thin-walled structures [6,8,11,19,29,31,39,47,53,54,64]. As the most popular methods used for the solution of contact problems for thin-walled structural elements, we can mention the conjugation method according to which the systems of key equations are solved separately in the contact zone and outside it with subsequent matching of the solutions; the semiinverse method, where, on the basis of some arguments used in the statement of the problem, we choose expressions for contact stresses with a certain collection of unknown parameters determined in the course of solving; the method of influence functions (Green's functions method), which makes it possible to reduce the problem of the evaluation of contact stresses to the solution of Fredholm or Volterra integral equations.…”

“…The works by Aleksandrov, Blokh, Vasylenko, Grigolyuk, Grigorenko, Hudramovych, Kit, Mossakovs'kyi, Mkhitaryan, Pelekh, Popov, Hills, et al [2,8,19,20,25,40,41,47,54,66,74] are devoted to the development of foundations of the mechanics of contact interaction of thin-walled structural elements and the methods used for the numerical analysis of the corresponding contact problems.…”