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Contact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter

НазваContact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter
Назва англійськоюContact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter
АвториHryhorii Habrusiev, Iryna Habrusieva
ПринадлежністьTernopil Ivan Puluj National Technical University, Ternopil, Ukraine
Бібліографічний описContact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter / Hryhorii Habrusiev, Iryna Habrusieva // Scientific Journal of TNTU. — Tern.: TNTU, 2021. — Vol 102. — No 2. — P. 87–95.
Bibliographic description:Habrusiev H., Habrusieva I. (2021) Contact interaction of a predeformed plate which lies without friction on rigid base with a parabolic indenter. Scientific Journal of TNTU (Tern.), vol 102, no 2, pp. 87–95.
УДК

539.3

Ключові слова

predeformed plate, prestressed layer, contact stresses, vertical displacements, parabolic indenter, dual integral equations.

Within the framework of linearized formulation of a problem of the elasticity theory, the stress-strain state of a predeformed plate, which is modeled by a prestressed layer, is analyzed in the case of its smooth contact interaction with a rigid axisymmetric parabolic indenter. The dual integral equations of the problem are solved by representing the quested-for functions in the form of a partial series sum by the Bessel functions with unknown coefficients. Finite systems of linear algebraic equations are obtained for determination of these coefficients. The influence of the initial strains on the magnitude and features of the contact stresses and vertical displacements on the surface of the plate is analyzed for the case of compressible and incompressible solids. In order to illustrate the results, the cases of the Bartenev – Khazanovich and the harmonic-type potentials are addressed.

ISSN:2522-4433
Перелік літератури
  1. Mahesh S., Selvamani R., Ebrahami F. Assessment of hydrostatic stress and thermo piezoelectrici-ty in a laminated multilayered rotating hollow cylinder. Mechanics of Advanced Composite Structures. 2021. Volume 8. Issue 1. P. 77–86.
  2. Jesenko M., Schmidt B. Geometric linearization of theories for incompressible elastic materials
    and applications. Mathematical Models and Methods in Applied Sciences. 2021. Volume 31. Issue 4.
    P. 829–860.
  3. Chen X., Dai H.-H., Pruchnicki E. On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method. Mathematics and Mechanics of Solids. 2021. Volume 26. Issue 2.
    P. 217–229.
  4. Babich S. Yu., Guz A. N., Rudnitskiy V. B. Kontaktnyie zadachi dlya uprugih tel s nachalnyimi napryajeniyami primenitelno k jestkim i uprugim shtampam. Prikl. mehanika. 2004. 40. No. 7. P. 41–69. [In Russsian].
  5. Habrusiev H. Habrusieva I., Shelestovs’kyi B. The effect of initial deformations of the thick plate on its contact interaction with the ring punch. Scientific Journal of TNTU. 2018. Vol. 90. No. 2. P. 50–59.
References:
  1. Mahesh S., Selvamani R., Ebrahami F. Assessment of hydrostatic stress and thermo piezoelectrici-ty in a laminated multilayered rotating hollow cylinder. Mechanics of Advanced Composite Structures. 2021. Volume 8. Issue 1. P. 77–86.
  2. Jesenko M., Schmidt B. Geometric linearization of theories for incompressible elastic materials
    and applications. Mathematical Models and Methods in Applied Sciences. 2021. Volume 31. Issue 4.
    P. 829–860.
  3. Chen X., Dai H.-H., Pruchnicki E. On a consistent rod theory for a linearized anisotropic elastic material: I. Asymptotic reduction method. Mathematics and Mechanics of Solids. 2021. Volume 26. Issue 2.
    P. 217–229.
  4. Babich S. Yu., Guz A. N., Rudnitskiy V. B. Kontaktnyie zadachi dlya uprugih tel s nachalnyimi napryajeniyami primenitelno k jestkim i uprugim shtampam. Prikl. mehanika. 2004. 40. No. 7. P. 41–69. [In Russsian].
  5. Habrusiev H. Habrusieva I., Shelestovs’kyi B. The effect of initial deformations of the thick plate on its contact interaction with the ring punch. Scientific Journal of TNTU. 2018. Vol. 90. No. 2. P. 50–59.
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