Просторова контактна задача про тиск пружного кільцевого штампа з початковими напруженнями на попередньо напружений півпростір
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Дата
2019
Автори
Ярецька, Наталія Олександрівна
Yaretska, N.A.
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Назва тому
Видавець
Херсонський національний технічний університет
Анотація
В рамках лінеаризованої теорії пружності представлено розв’язок контактної задачі про тиск пружного кільцевого штампа з початковими напруженнями на попередньо напружений півпростір без урахування сил тертя. Дослідження представлено у загальному вигляді для теорії великих початкових деформацій і двох варіантів теорії малих початкових деформацій при довільній структурі пружного потенціалу для рівних коренів визначального рівняння. Числова реалізація методу дала змогу графічно відобразити вплив початкових напружень на закон розподілу контактних характеристик тіл, для потенціалів найпростішої структури.
The article is devoted to the study of the contact interaction of a pre-stressed annular stamp and a halfspace with initial stresses without taking friction forces into account. The problem is solved for the case of equal roots of the resolving equation. The study is presented in a general form for the theory of large initial (finite) deformations and two versions of the theory of small initial deformations in the framework of the linearized theory of elasticity for an arbitrary structure of the elastic potential. There is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. Also, it is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials. Numerical analysis is presented by the form of graphs and tables of contact stresses and displacements of a potential for a harmonic type. The algorithm for solving this problem is implemented in the form of a computer program (Maple 17). The influence of the initial stress on the contact interaction between the elastic annular stamp and the elastic half-space of the potentials of a particular structure is investigated. The value of the studies carried out is that taking into account the influence of the initial stresses in the bodies on the law of distribution of the contact characteristics of elastic bodies at the points of their interaction can allow us to take into account, more effectively, the wear resistance of materials by properly estimating their strength reserves. Also, it can sufficiently reduce their material consumption, while retaining the necessary functional characteristics of materials.
The article is devoted to the study of the contact interaction of a pre-stressed annular stamp and a halfspace with initial stresses without taking friction forces into account. The problem is solved for the case of equal roots of the resolving equation. The study is presented in a general form for the theory of large initial (finite) deformations and two versions of the theory of small initial deformations in the framework of the linearized theory of elasticity for an arbitrary structure of the elastic potential. There is assumed that the initial states of the elastic annular stamp and the elastic half-space remain homogeneous and equal. The study is carried out in the coordinates of the initial deformed state, which are interrelated with Lagrange coordinates (natural state). In addition, the influence of the annular stamp causes small perturbations of the basic elastic deformed state. Also, it is assumed that the elastic annular stamp and the elastic half-space are made of different isotropic, transversal-isotropic or composite materials. Numerical analysis is presented by the form of graphs and tables of contact stresses and displacements of a potential for a harmonic type. The algorithm for solving this problem is implemented in the form of a computer program (Maple 17). The influence of the initial stress on the contact interaction between the elastic annular stamp and the elastic half-space of the potentials of a particular structure is investigated. The value of the studies carried out is that taking into account the influence of the initial stresses in the bodies on the law of distribution of the contact characteristics of elastic bodies at the points of their interaction can allow us to take into account, more effectively, the wear resistance of materials by properly estimating their strength reserves. Also, it can sufficiently reduce their material consumption, while retaining the necessary functional characteristics of materials.
Опис
https://mkmm.org.ua/archive_mkmm/
Ключові слова
лінеаризована теорія пружності, початкові (залишкові) напруження, контактна задача, кільцевий штамп, півпростір, the linearized elasticity theory, initial (residual) stresses, contact problem, annular punch, half-space
Бібліографічний опис
Ярецька Н. О. Просторова контактна задача про тиск пружного кільцевого штампа з початковими напруженнями на попередньо напружений півпростір. / Н. О. Ярецька // Вісник Херсонського національного технічного університету. – Херсон : ХНТУ, 2019. – № 2 (69), ч. 2. – С. 134–140.