Boundary layers on the upper/lower surfaces of reinforced plates

Authors

  • Boris D. Annin Lavrentiev Institute of Hydrodynamics, 15, pr. Akademika Lavrentieva, Novosibirsk, 630090, Russian Federation
  • Aleksandr G. Kolpakov SysAn - System Analysis in Engineering, 12, ul. A. Nevskogo, Novosibirsk, 630075, Russian Federation
  • Sergey I. Rakin Siberian Transport University, 191, ul. Dusi Kovalchuk, Novosibirsk, 630090, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.301

Abstract

The periodicity cell problems of the homogenization theory, both elastic and thermoelastic, are discussed for a fiber-reinforced plate. A feature of the periodicity cells of the plates is the presence of free surfaces in them. As follows from our calculations, boundary layers appear on free surfaces. The characteristics of these boundary layers for unidirectional and transverse reinforced plates are investigated.

Keywords:

plate, reinforcing fibers, matrix, homogenization method

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References

Литература

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36. Kang H., Yu S. A proof of the Flaherty-Keller formula on the effective property of densely packed elastic composites. Calc. Var. 59, 22 (2020). https://doi.org/10.1007/s00526-019-1692-z

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42. Kolpakov A.A., Kolpakov A.G. Solution of the laminated plate design problem: new problems and algorithms. Computers & Structures 83 (12-13), 964-975 (2005). https://doi.org/10.1016/j.compstruc.2004.08.012

43. Kolpakov A.A. Design of a Laminated Plate Possessing the Required Stiffnesses Using the Minimum Number of Materials and Layers. J. Elasticity 86, 245-261 (2007). https://doi.org/10.1007/s10659- 006-9092-y

44. Cao S., Zhang J., Wu J., Chen J. Analysis of orange peel defect in St14 steel sheet by electron backscattered diffraction (EBSD). J. Mater. Sci. Technology 21, 17-20 (2005).

45. Vonach W., Rammerstorfer F. A general approach to the wrinkling instability of sandwich plates. Struct. Eng. Mech. 12 (4), 363-376 (2001). https://doi.org/10.12989/sem.2001.12.4.363

46. Vescovini R., D’Ottavio M., Dozio L., Polit O. Buckling and wrinkling of anisotropic sandwich plates. Int. J. Eng. Sci. 130, 136-156 (2018). https://doi.org/10.1016/j.ijengsci.2018.05.010

Published

2022-10-10

How to Cite

Annin, B. D., Kolpakov, A. G., & Rakin, S. I. (2022). Boundary layers on the upper/lower surfaces of reinforced plates. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(3), 391–404. https://doi.org/10.21638/spbu01.2022.301

Issue

Section

On the anniversary of N.F. Morozov