Simulation of a pre-deformed plate compression by two indenters of complex shape
| Назва | Simulation of a pre-deformed plate compression by two indenters of complex shape |
| Назва англійською | Simulation of a pre-deformed plate compression by two indenters of complex shape |
| Автори | Hryhorii Habrusiev, Iryna Habrusieva, Borys Shelestovskyi |
| Принадлежність | Ternopil Ivan Puluj National Technical University,Ternopil, Ukraine |
| Бібліографічний опис | Simulation of a pre-deformed plate compression by two indenters of complex shape / Hryhorii Habrusiev, Iryna Habrusieva, Borys Shelestovskyi // Scientific Journal of TNTU. — Tern.: TNTU, 2023. — Vol 112. — No 4. — P. 91–101. |
| Bibliographic description: | Habrusiev H., Habrusieva I., Shelestovskyi B. (2023). Simulation of a pre-deformed plate compression by two indenters of complex shape. Scientific Journal of TNTU (Tern.), vol 112, no 4, pp. 91–101. |
| УДК | 539.3 |
| Ключові слова | pre-deformed plate, pre-stressed layer, contact stresses, vertical displacements, complex form indenter, dual integral equations. |
Within the framework of linearized formulation of the elasticity theory problems, the stress-strain state of a pre-deformed plate, which is modeled by a pre-stressed layer, is analyzed in the case of its smooth contact interaction with a two rigid axisymmetric indenters. 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. Lapusta Y., Harich J., Wagner W. Three-dimensional FE model for fiber interaction effects during microbuckling in composites with isotropic and anisotropic fibers. Commun. Numer. Meth. Eng. 2008. 24, No. 12. P. 2206–2215.
2. Mahesh S., Selvamani R. and 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.
3. 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.
4. Diandian Gu, Chenbo Fu, Hui-Hui Dai, K.R. Rajagopal, Asymptotic beam theory for non-classical elastic materials. International Journal of Mechanical Sciences. Volume 189. 2021. 105950, ISSN 0020-7403, URL: https://doi.org/10.1016/j.ijmecsci.2020.105950.
5. 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. P. 87–95.
6. Habrusiev H., Habrusieva I., Shelestovs’kyi B. (2018). The effect of initial deformations of the thick plate on its contact interaction with the ring punch. Scientific Journal of TNTU (Tern.). Vol. 90. No. 2. P. 50–59.
7. A. N. Guz’ and V. B. Rudnitskii, Foundations of the Theory of Contact Interaction of Elastic Bodies with Initial (Residual) Stresses, PP Mel’nik, Khmel’nitskii (2006) P. 710. [In Russian]. |
| References: |
1. Lapusta Y., Harich J., Wagner W. Three-dimensional FE model for fiber interaction effects during microbuckling in composites with isotropic and anisotropic fibers. Commun. Numer. Meth. Eng. 2008. 24, No. 12. P. 2206–2215.
2. Mahesh S., Selvamani R. and 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.
3. 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.
4. Diandian Gu, Chenbo Fu, Hui-Hui Dai, K.R. Rajagopal, Asymptotic beam theory for non-classical elastic materials. International Journal of Mechanical Sciences. Volume 189. 2021. 105950, ISSN 0020-7403, URL: https://doi.org/10.1016/j.ijmecsci.2020.105950.
5. 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. P. 87–95.
6. Habrusiev H., Habrusieva I., Shelestovs’kyi B. (2018). The effect of initial deformations of the thick plate on its contact interaction with the ring punch. Scientific Journal of TNTU (Tern.). Vol. 90. No. 2. P. 50–59.
7. A. N. Guz’ and V. B. Rudnitskii, Foundations of the Theory of Contact Interaction of Elastic Bodies with Initial (Residual) Stresses, PP Mel’nik, Khmel’nitskii (2006) P. 710. [In Russian]. |
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