Study of stress-strain state of the transversely isotropic plates using the refined theory
Keywords:
transversely isotropic plates; refined theory; the equations of statics; fundamental solution; special G-function
Abstract
The fundamental solution of statics equations of transversely isotropic plate was obtained using the two-dimensional Fourier integral transform and the inversion technic based on the special G-function. Such method allows reducing the system of resolving differential equations, which describe static state of flat plate or shell, to a system of algebraic equations. Then, the inverse Fourier transform restores the fundamental solution. Numerical studies, which were carried out, have detected the behavior patterns of stress-strain state components in dependence on material elastic constants. This approach demonstrates development of refined theory of plates and shells based on the three-dimensional elasticity theory.
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References
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Goldenveizer, A. L. Research of the stress condition of the spherical shell. Applied Mathematics and Mechanics, Vol. 6, 441–467, 1944.
Łukasiewicz, S. A. Introduction of concentrated loads in plates and shells. Progress in Aerospace Sciences, Vol. 17, 109–146, 1976.
Darevskii, V. M. Contact problems of the theory of shells (the action of local loads on the shell). Proceedings of VI All-Union Conference on the theory of shells and plates. M.: Nauka, 927–933, 1966.
Zhigalko, Y. P. Calculation of thin elastic cylindrical shells at local loads (literature review, methods and results). Investigations in the theory of plates and shells, Vol. 4, 3–41, 1966.
Bokov, I.P., Strelnikova, E.A. Construction of the fundamental solution of the equations of statics isotropic plates using the theory of S.P. Tymoshenko. Bulletin of V. Karazin Kharkiv National University, №1156, 29-35, 2015.
Han, H. Elasticity Theory: Fundamentals of linear theory and its application. M.: World, 344, 1988.
Pelekh, B. L., Lazko, V. A. Laminated anisotropic plates and shells with stress concentrators. K.: Science thought, 296, 1982.
Vladimirov, V. S. Generalized functions in mathematical physics. M.: Science, 280, 1976.
Sneddon, I. Fourier transform. M.: Foreign literature publishing house, 668, 1955.
Khizhnyak, V. K., Shevchenko, V. P. Mixed problem in the theory of plates and shells. DonGU: Donetsk, 128, 1980.
Dementyev, A. D., Nazarov, L. A., Nazarova, L. A. Applications of the theory of elasticity. Novosibirsk, 224, 2002.
Published
2015-10-26
How to Cite
Bokov, I. P., Bondarenko, N. S., & Strelnikova, E. A. (2015). Study of stress-strain state of the transversely isotropic plates using the refined theory. Bulletin of V.N. Karazin Kharkiv National University, Series «Mathematical Modeling. Information Technology. Automated Control Systems», 27, 33-40. Retrieved from https://periodicals.karazin.ua/mia/article/view/14192
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