Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler
https://doi.org/10.21822/2073-6185-2021-48-2-124-132
Abstract
Objective. In most cases, when determining the stress-deformed state of three-layer structures, it is assumed that bearing layers obey the Kirchhoff-Love hypothesis, while a filler obey the Neit (vanderNeit), or “broken line”, hypothesis. But in many cases, the results of our research show that this is not always accurate.
Methods. It is proposed to solve the three-dimensional problem of determining the stress-deformed state of a three-layer structure using cubic functions of the law of aggregate deformation distribution along the normal line, obtained on the basis of the law of deformation compatibility at “filler – bearing layer” boundaries and the construction of boundary conditions in joint zones.
Results. Equilibrium equations of a three-layer beam obtained on the basis of this hypothesis are shown in Table 1. The given partial differential equations are of the 12th order and we transformed them into homogeneous equations of the 1st order to simplify the solution. This solution is implemented using the mathematical modelling software package Mаple 5.4.
Conclusion. The work of the filler in the direction of OX axis has a certain value, which affects the overall stress state of the three-layer structure (in existing hypotheses, it is zero).
About the Authors
O. M. Ustarkhanov
Daghestan State Technical University
Russian Federation
Russian Federation
70 I. Shamilya Ave., Makhachkala 367026
Kh. M. Muselemov
Daghestan State Technical University
Russian Federation
Russian Federation
Khairulla M.Muselemov, Cand.Sci. (Technical), Assoc. Prof., Department of Building Structures and Hydraulic Structures
70 I. Shamilya Ave., Makhachkala 367026
Kh. M. Gapparov
Daghestan State Technical University
Russian Federation
Russian Federation
Khizri M. Gapparov, Postgraduate Student, Department of Building Materials and Engineering Networks
70 I. Shamilya Ave., Makhachkala 367026
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Review
For citations:
Ustarkhanov O.M., Muselemov Kh.M., Gapparov Kh.M. Stress-deformed state of a three-layer structure taking into account the hypothesis of cubic displacement pattern over the thickness of a filler. Herald of Dagestan State Technical University. Technical Sciences. 2021;48(2):124-132. (In Russ.) https://doi.org/10.21822/2073-6185-2021-48-2-124-132
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