Original equations of a geometrically nonlinear dynamic problem of essential deformation for axisymmetric and flat bodies
DOI:
https://doi.org/10.32347/2410-2547.2019.102.252-262Keywords:
body of rotation, geometric nonlinearity, physical nonlinearity, plastic deformation, contact stress, dynamic loadAbstract
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.
References
Blokh V.I. Teoriya uprugosti (Theory of Elasticity) / [Blokh V.I.] - Khar'kov: Izd-vo Khar'k. un-ta.- 1964. –483s.
Vol'mir A.S. Statika i dinamika slozhnykh struktur: Prikladnyye mnogourovnevyye metody issledovaniy (Statics and dynamics of complex structures: Applied multilevel research methods) / [Vol'mir A.S., Kuranov B.A., Turbaivskiy A.T.] – M.: Mashinostroyeniye, 1989. –248s.
Drukker D. Variatsionnyye printsipy v matematicheskom teorii plastichnosti (Variational principles in the mathematical theory of plasticity) / [Drukker D.] - Mekhanika.- M.: IP, 1959.- № 6.
Lurie A.I. Neliniyna teoriya pruzhnosti(Nonlinear theory of elasticity) / [Lurie A.I.] - M .: Nauka, 1980, 512s.
Malikin M.M. Prykladna teoriya plastychnosti ta povzuchosti (Applied theory of plasticity and creep) / [Malikin M.M.] -Vid. Machine-building, Moscow, 1975, 399s.
Pozdeev A.A. Velyki pruzhnoplastychni deformatsiyi. (Large elastoplastic deformations) / [Pozdeev A.A., Trusov PV, Nyashin Yu.I.] -M., Science, 1986, 232s.
Sakharov A.S. Metod konechnykh elementov v mekhanike tverdykh tel (The finite element method in solid mechanics) / [Sakharov A.S., Kislookiy V.N., Kirichevskiy V.V. i dr.] - Kiyev: Vishcha shkola, 1982.- 479 s.
Torkhamov M.M. Pro zvyazok mizh napruzhennyamy ta skinchennymy plastychnymy deformatsiyamy pry prostomu navantazhenni v prostori istynnykh napruzhen (On the connection between stresses and finite plastic deformations with simple loading in the space of true stresses) / Ed. "Prikl.Meh.", Kyiv, 1985, - 13s. Manuscript dep. In VINITI, No. 7899-V
Tormakhov M.M. Perevirka postulatu izotropiyi v oblasti skinchennykh prozhno-plastychnykh deformatsiy (Verification of the isotropy postulate in the area of finite forging-plastic deformations) / Kiev. Institute of Mechanics of the Academy of Sciences of USSR, 1985, 6s. Manuscript dep. In VINITI, 1986, No. 5507В86
Downloads
Published
Issue
Section
License
Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
