Construction of fundamental solution of static equations of medium-thickness isotropic plates

Authors

  • Игорь Петрович Боков A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharsky Str. 2/10, Kharkov, Ukraine, 61046, Ukraine https://orcid.org/0000-0002-9138-4120
  • Елена Александровна Стрельникова A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharsky Str. 2/10, Kharkov, Ukraine, 61046, Ukraine https://orcid.org/0000-0003-0707-7214

DOI:

https://doi.org/10.15587/1729-4061.2015.47232

Keywords:

refined theory, isotropic plates, static equations, force actions, special G-function

Abstract

A fundamental solution of the elasticity theory equations for isotropic plates was obtained. To construct the two-dimensional elasticity theory equations, the approximation method of displacements, stresses and strains using Fourier series by Legendre polynomials on the transverse coordinate was used. This approach has allowed to take into account the transverse shear and normal stresses. Since the classical Kirchhoff-Love theory does not consider these stresses, the research based on the refined theories of the stress-strain state of isotropic plates under concentrated force actions is an urgent scientific and technical problem. The fundamental solution of these equations was found using the two-dimensional Fourier integral transform and the generalization method, built with a special G-function. The method allows to reduce the system of resolvent differential static equations of flat plates and shells to a system of algebraic equations. Then the inverse Fourier transform restores fundamental solution. Numerical studies that demonstrate behavior patterns of the stress-strain state components depending on the elastic constants of isotropic material were performed. The approach demonstrates the development of the refined theory of plates and shells based on the three-dimensional elasticity theory.

Author Biographies

Игорь Петрович Боков, A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharsky Str. 2/10, Kharkov, Ukraine, 61046

PhD student

Department of Applied Mathematics and Mathematical Modeling

Елена Александровна Стрельникова, A. N. Podgorny Institute of Mechanical Engineering Problems NAS of Ukraine Pozharsky Str. 2/10, Kharkov, Ukraine, 61046

Professor, Doctor of Technical Sciences, Senior Researcher

Department of Strength and Optimization

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Published

2015-08-19

How to Cite

Боков, И. П., & Стрельникова, Е. А. (2015). Construction of fundamental solution of static equations of medium-thickness isotropic plates. Eastern-European Journal of Enterprise Technologies, 4(7(76), 27–34. https://doi.org/10.15587/1729-4061.2015.47232

Issue

Vol. 4 No. 7(76) (2015): Applied mechanics

Section

Applied mechanics

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Copyright (c) 2015 Игорь Петрович Боков, Елена Александровна Стрельникова

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