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 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]: Year: Volume: Issue: Page: Find

 Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, Volume 22, Number 2, Pages 325–343 (Mi vsgtu1610)

Mathematical Modeling, Numerical Methods and Software Complexes

Mathematical modeling of dynamic deformation of elasto-viscoplastic shells of finite lenght by a ray method

N. D. Verveiko, M. V. Egorov*

Voronezh State University, Voronezh, 394006, Russian Federation

Abstract: The paper presents a mathematical modeling of dynamic stress-strain state of the rotation of the shell elasto-viscoplastic material. We solve the modified system of S. P. Timoschenko's partial differential equations by constructing a system of equations on moving surfaces of the gap with the initial conditions in the form of a shock at the end, written in the form of a power series in time, whose coefficients have initial conditions for the differential equations. The solution is presented in the form of the Taylor's row series up to the fourth order in the shell coordinate. To simulate the waves reflected from the boundaries, the conditions at the boundary of two types (rigidly restrained and stress-free), independent of time, are introduced. A set of programs written in Fortran 90 on the Code::Blocks platform is developed. Two programs for the simulation of dynamic deformation of shell in elastic and elasto-viscoplastic state are implemented. We use the difference representation of the derivatives, the calculation of the integrals by the trapezoid method with a given step of partitioning the segment. The result of the programs is the grid functions of the coefficients of the Taylor rows, which are used to construct the displacement graphs as functions of time and the longitudinal coordinate of the shell.

Keywords: dynamic deformation, rotating shell, ray method, reflected wave, modeling, elasticity, viscosity, plasticity.
* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1610

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Bibliographic databases:

UDC: 539.3
MSC: 74H15, 65Z05
Revised: May 21, 2018
Accepted: June 11, 2018
First online: July 1, 2018

Citation: N. D. Verveiko, M. V. Egorov, “Mathematical modeling of dynamic deformation of elasto-viscoplastic shells of finite lenght by a ray method”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:2 (2018), 325–343

Citation in format AMSBIB
\Bibitem{VerEgo18} \by N.~D.~Verveiko, M.~V.~Egorov \paper Mathematical modeling of dynamic deformation of elasto-viscoplastic shells of finite lenght by a ray method \jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.] \yr 2018 \vol 22 \issue 2 \pages 325--343 \mathnet{http://mi.mathnet.ru/vsgtu1610} \crossref{https://doi.org/10.14498/vsgtu1610} \zmath{https://zbmath.org/?q=an:07038288} \elib{https://elibrary.ru/item.asp?id=35467733}