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Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
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IssuesArchive of Issues2015-5pp.475-492

Archive of Issues

Since 2018, translations of PMM's articles have been published in special issues of the journals Mechanics of Solids and Fluid Dynamics:

Total articles in the database: 1923
In Russian (): 1124
In English (J. Appl. Math. Mech.): 799

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A.P. Yankovskii, "Refinement of the asymptotic expansions when solving the spatial problem of the bending and twisting of composite bars," J. Appl. Math. Mech. 79 (5), 475-492 (2015)
Year 2015 Volume 79 Issue 5 Pages 475-492
DOI 10.1016/j.jappmathmech.2016.03.009
Title Refinement of the asymptotic expansions when solving the spatial problem of the bending and twisting of composite bars
Author(s) A.P. Yankovskii (S.A. Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia,
Abstract A linear elastic problem of the static deformation of laminated composite bars of constant cross-section is formulated in dimensionless form in three dimensions without taking account of thermal effects and mass loads. An asymptotic representation of the solution of the problem, that is more complete than the previous representation and enables the spatial stress-strain state of composite bars to be determined beyond the limits of boundary layer zones, is constructed within the framework of the method of rigidity functions proposed by Gorynin and Nemirovskii. The relative thickness of the bar is used as a small geometric parameter. The two-dimensional and one-dimensional boundary value problems arising after decomposing the initial three-dimensional equations for the bending and twisting of composite bars are analysed. Analytical solutions are obtained for several two-dimensional boundary value problems determining the characteristic displacement functions when Poissons ratios of all the layers are identical. Certain effective rigidities of a composite bar under different forms of loading and deformation are calculated for this case in explicit form.
Received 29 August 2014
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