INVESTIGATION OF STRESS-STRAIN STATE OF TRANSVERSELY ISOTROPIC PLATES UNDER BENDING USING EQUATION OF STATICS {1,2} –APPROXIMATION

Igor Bokov, Natalia Bondarenko, Elena Strelnikova

Abstract


The study examined the construction of the fundamental solution for the equations of statics {1,2} approximation for transversely isotropic plates under bending with the action of concentrated force. Equations {1,2} -approximation were obtained by the decomposition method in the thickness coordinate using the Legendre polynomials. These equations take into account all the components of the stress tensor, including the transverse shear and normal stresses. Since the classical theory of Kirchhoff-Love doesn’t take account of these stresses, the study on the basis of refined theories of stress-strain state of transversely isotropic plates under the action of concentrated force effects is an important scientific and technical problem.

The fundamental solution of obtained equations results using a two-dimensional Fourier integral transform and inverse treatment techniques, built with the help of a special G-function. This method allows reducing the system of resolving differential equations for statics of flat plates and shells to a system of algebraic equations. After that, the inverse Fourier transform restores the fundamental solution. The work was carried out numerical studies that demonstrate patterns of behavior of components of the stress-strain state, depending on the elastic constants of transversely isotropic material. The results play a decisive role in the study of boundary value problems in the mechanics of thin-walled elements of constructions, including under the influence of concentrated and local diverse forces.

Keywords


{1;2} -approximation; equations of statics; transversely isotropic plates; concentrated force; bending state

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References


Pogorelov, V. I. (2007). Structural Mechanics of thin-walled structures: a tutorial. Saint Peterburg: BHV-Petersburg, 518.

Bashev, V. F., Sukhov, E. V., Syrovatko, J. V. (2012). Statistical analysis of microstructure of composite materials. Starodubovskie reading, 53–57.

Pelekh, B. L., Lazko, V. A. (1982). Laminated anisotropic plates and shells with stress concentrators. Kyiv: Science. Dumka, 296.

Bokov, I. P., Strelnikova, E. A. (2015). Fundamental solution of static equations of transversely isotropic plates. International Journal of Innovative Research in Engineering and Management, 2 (6), 56–62.

Bokov, I. P., Bondarenko, N. S., Strelnikova, E. A. (2016). Construction of the fundamental solution of the equations of statics {1,2}-approximation the membrane stress state for transversely isotropic plates. ScienceRise, 8 (2 (25)), 41–48. doi: 10.15587/2313-8416.2016.76534

Bondarenko, N. S., Goltsev, A. S. (2015). Research incision influence the stress intensity factors in an isotropic plate on the basis of the generalized theory. Proceedings of the Institute of Applied. Mathematics and Mechanics, 29, 20–28.

Bondarenko, N. S., Goltsev, A. S. (2010). Fundamental solutions of the equations of thermoelasticity transversely isotropic plates. Journal of Applied Mechanics, 46 (3), 51–60.

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.

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: a tutorial. Donetsk: DonGU, 128.




DOI: http://dx.doi.org/10.21303/2461-4262.2016.00159

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ISSN 2461-4262 (Online), ISSN 2461-4254 (Print)