Analysis of fundamental solutions to the equations of statics constructed for transversal-isotropic plates

Authors

  • Igor Bokov A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046, Ukraine https://orcid.org/0000-0002-9138-4120
  • Natalia Bondarenko A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046, Ukraine
  • Elena Strelnikova A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046, Ukraine https://orcid.org/0000-0003-0707-7214

DOI:

https://doi.org/10.15587/1729-4061.2017.96508

Keywords:

{m, n}-approximation, force impact, equation of statics, transversal-isotropic plate, Legendre polynomials

Abstract

In present research, we examined and analyzed the fundamental solutions of the equations of statics for the transversal-isotropic plates, which were built using generalized theory of the {m,n}-approximation. The methods for reducing the three-dimensional problems of the theory of elasticity to the two-dimensional ones are explored. In the study, we analyzed results, obtained on the basis of theory of the {m,n}-approximation, for the purpose of determining the refinement, which is introduced by the retention of a large number of terms in the expansion series of the desired functions. This theory is the most preferable for reducing the three-dimensional equations of the theory of elasticity to the two-dimensional ones since it is not based on any hypotheses, but employs the method of I. N. Vekua for the expansion of the desired functions into the Fourier series by the Legendre polynomials. This approach makes it possible to examine not only the thin plates, but also the plates of medium and large thickness, and allows us to consider transverse shearing and normal stresses. Since the classical theory of Kirchhoff–Love does not take these stresses into account, then examining on the basis of the refined theories of the stressed-strained state of transversal-isotropic plates under the action of concentrated force impacts is a relevant scientific and technical task. We carried out numerical studies that make it possible to determine the refinement, which is introduced by the retention of a large number of terms in the expansion series of the desired functions and to analyze the character of behavior of internal force factors of the zero spin stressed state and the state of bending, obtained with the use of generalized theory of the {1,0}- and {1,2}-approximation.

The obtained results play a decisive role when exploring different boundary problems of the mechanics of thin-walled elements of structures, including those exposed to the concentrated and local diverse actions.

Author Biographies

Igor Bokov, A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046

Postgraduate student

Department of General Research in Power Engineering

Natalia Bondarenko, A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046

PhD

Elena Strelnikova, A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharskoho str., 2/10, Kharkiv, Ukraine, 61046

Doctor of Technical Sciences, Professor, Senior Researcher

Department of General Research in Power Engineering

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Published

2017-04-29

How to Cite

Bokov, I., Bondarenko, N., & Strelnikova, E. (2017). Analysis of fundamental solutions to the equations of statics constructed for transversal-isotropic plates. Eastern-European Journal of Enterprise Technologies, 2(7 (86), 4–12. https://doi.org/10.15587/1729-4061.2017.96508

Issue

Vol. 2 No. 7 (86) (2017): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2017 Igor Bokov, Natalia Bondarenko, Elena Strelnikova

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