Construction of fundamental solution of {1,2}-approximation static equations of momentless stress state for transversely-isotropic plates
DOI:
https://doi.org/10.15587/2313-8416.2016.76534Keywords:
{1, 2}-approximation, fundamental solution, transversely-isotropic plates, static equations, momentless stress stateAbstract
The problem of static for transversely-isotropic plates, which are under the action of a concentrated force, was considered. Static equations of {1,2}-approximation obtained by decomposition of the desired functions in Fourier series in Legendre polynomials in relation to the thickness of the coordinates were used. These equations take into account all the components of the stress tensor, including the transverse shear and normal stresses. Numerical studies demonstrating the effect of elastic constants on the components of the stress-strain state of a transversely- isotropic plate were conducted
References
Vekua, I. N. (1955). A method for calculating prismatic shells. Pr. Tbilis. Mat. Inst., 21, 191–253.
Goldenveizer, A. L. (1954). On the question of the calculation of shells on concentrated forces. Appl. mathematics and mechanics, 8 (2), 181–186.
Vekua, I. N. (1970). Variational principles of the theory of shells. Tbilisi: Publisher of Tbilisi, 300.
Reissner, E. (1985). Reflections on the Theory of Elastic Plates. Applied Mechanics Reviews, 38 (11), 1453. doi: 10.1115/1.3143699
Kiel, N. A. (1973). On the action of local loads on the shell. Proceedings of the universities. Construction and architecture, 3, 43–46.
Velichko, P. M., Khizhnyak, V. K., Shevchenko, V. P. (1975). Local stresses in the shells of positive, neutral and negative curvature. Vol. 1. Tbilisi: Publishing house Mitsniereba, 31–41.
Bokov, I. P., Strelnikova, E. A. (2015). Fundamental solution of static equations of transversely isotropic plates. International Journal of Innovative Research in Engineering & Management, 2 (6), 56–62.
Bondarenko, N. S. (2009). The fundamental solution of differential equations of thermoelasticity {1,0}-approximation for transversely isotropic plates. Proceedings of the Institute of Applied Mathematics and Mechanics of National Academy of Sciences of Ukraine, 18, 11–18.
Bondarenko, N. S., Goltsev, A. S., Shevchenko, V. P. (2009). Fundamental solution {1,2}-approximation the membrane thermoelastic state transversely isotropic plates. Reports of National Academy of Sciences of Ukraine, 11, 46–52.
Bondarenko, N. S., Goltsev, A. S. (2014). Investigation of the influence of the environment on the state of isotropic thermoelastic plate with insulated cut at one-sided heat exchange. Theoretical and Applied Mechanics, 09 (55), 42–52.
Bondarenko, N. S. (2013). Stress intensity factor in a thermoelastic bending of isotropic plates with insulated cut in the case of a symmetrical heat. Mess. Of Donets. the University. Ser. A., 2, 20–26.
Vladimirov, V. S. (1976). Generalized functions in mathematical physics. Moscow: Science, 280.
Sneddon, I. (1955). Fourier transform. Moscow: Foreign literature publishing house, 668.
Khizhnyak, V. K., Shevchenko, V. P. (1980). Mixed problem in the theory of plates and shells. Donetsk: DonGU, 128.
Downloads
Published
Issue
Section
License
Copyright (c) 2016 Игорь Петрович Боков, Наталья Сергеевна Бондаренко, Елена Александровна Стрельникова
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
