Original equations of a geometrically nonlinear dynamic problem of essential deformation for axisymmetric and flat bodies

Widely used in various fields of technology are the elements and details that are in the process of manufacturing or operating in conditions of significant plastic deformation. This is typical of sealing ring gaskets, rivets in connecting operations, blanks in metal processing, etc. As a rule, the mechanical processes under consideration occur under the influence of intense dynamic loads. Significantly, deformation is also influenced by the condition of their interaction with the contacting parts of the instrument. Further improvement of the constructive decisions of a significant number of responsible nodes and technological processes largely depends on the completeness and reliability of the information on the peculiarities of changing the pattern of the stress-strain state of the selected class of objects in the process of deformation.In recent years, the requirements for the construction of mechanical models for the study of the processes of manufacturing and operating components and equipment has grown significantly, which is determined by increasing the level of accuracy and reliability of the results, prompting the use of more and more detailed calculation schemes. In addition, the difficulties of studying the behavior of structures in the presence of dynamic loads is multiplied by comparison with static analysis.In this connection, the importance of developing effective methods for studying the processes of plastic molding of bodies, taking into account geometric nonlinearity and contact interaction under the action of dynamic loads, increases.The paper considers the original equations of a geometrically nonlinear dynamic problem for the study of processes of significant plastic deformation. The problem statement is given under the condition of contact interaction of bodies. The equations of state are presented in the reference initial, changeable and actual coordinate systems.
В роботі розглянуто вихідні співвідношення геометрично нелінійної задачі динамікидля дослідження процесів істотного пластичного деформування.Наведена постановка задачі при умові контактної взаємодії тіл. Представлені рівняння стану у відліковій початковій, відліковій змінній та актуальній системах координат.