Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 22, no. 1, 2019 (March)
Pages 24-32
Cited by J. of Mech. Eng., 2019, vol. 22, no. 1, pp. 24-32



Stanislav B. Kovalchuk, Poltava State Agrarian Academy (1/3, Skovorody Str., Poltava, 36003, Ukraine), e-mail:, ORCID: 0000-0003-4550-431X

Oleksii V. Goryk, Poltava State Agrarian Academy (1/3, Skovorody Str., Poltava, 36003, Ukraine), ORCID: 0000-0002-2804-5580



The development of composite technologies contributes to their wide introduction into the practice of designing modern different-purpose structures. Reliable prediction of the stress-strain state of composite elements is one of the conditions for creating reliable structures with optimal parameters. Analytical theories for determining the stress-strain state of multilayer rods (bars, beams) are significantly inferior in development to those for composite plates and shells, although their core structural elements are most common. The purpose of this paper is to design an analytical model for bending double support multilayer beams under a concentrated load, with the model based on the previously obtained elasticity theory solution for a multi-layer cantilever. The second part of the article contains examples of the implementation of the model for bending double-support multi-layer beams under a concentrated load, with the model constructed in the first part of the article. Using this model, solutions to the problems of bending multi-layer beams with different types of fixation of their extreme cross-sections were obtained. The resultant relations were approbated using test problems for determining the deflections of homogeneous composite double-support beams with different combinations of fixation, as well as in determining the stresses and displacements of a four-layer beam with a combination of a rigid and hinged fixation at its ends. The results obtained have a slight discrepancy with the simulation results by the finite element method (FEM) and the calculation by the iterative model for bending composite bars, even for relatively short beams. In addition, it is shown that the neglect of the shear amenability of layer materials results in large errors in determining the deflections, and in the case of statically indefinable beams, reactive forces and stresses. The approach used in the construction of the model can be extended to the case of beams with arbitrary numbers of concentrated forces and intermediate supports, and to calculate multilayer beams with different rigidity of their design sections.


Keywords: multilayer beam, orthotropic layer, concentrated load, deflection, stresses, displacements.


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Received 26 September 2018

Published 30 March 2019