The peculiarities in contact interaction and wear of thin-walled elements of construction

Abstract

Розглянуто контактні задачі для тонкостінних елементів конструкцій і їхнього зношування. Запропоновано єдину методику розв'язування задач, яка базується на зведенні до інтегральних рівнянь Вольтерра. Це дає змогу виявити особливості розв'язків залежно від гіпотез, які характеризують деформування тонкостінного елемента. Наведено розв'язки та аналіз задач зношування пластин жорстким штампом, гарячим штампом, з урахуванням фрикційного розігріву, з урахуванням зміни товщини пластини у процесі зношування.

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

“…On the basis of the general approach, the main relations of the theory of transversely isotropic plates of variable thickness that take into account the phenomenon of compression of the element normal to the middle surface, shear strains, and boundary conditions on the faces were obtained in [38,39]. In the {1,0}-approximation, these relations take the following form in a Cartesian coordinate system: − the balance equations:…”

“…For the analysis of the specific features of formulation and solution of contact problems for plates and shells, depending on the theory used to describe the stress-strain state, we proposed to use the method of Volterra integral equations. A numerical-analytic approach to the solution of contact problems was developed in [38,39]. The efficiency of this approach was demonstrated by analyzing the problems of contact stiffness of specific structural joints [28].…”

“…The investigation of the process of wear of transversely isotropic plates by rigid punches was performed with the use of the developed approaches [35].…”

“…To describe the stress-strain state of the plate, we use the generalized theory with regard for compression and shear strains (7)−( 9). In the case of contact interaction with wear, the integral equation takes the form [35]…”

“…To solve the integral equation ( 14), we used an approximate step-by-step method with respect to time t . The interval of integration is split into sufficiently short segments, and the problems are solved in each of these segments [35]. It is assumed that, in these intervals, the unknown quantities are independent of time.…”