For citation:
Akopyan A. G. The flexural strength of anisotropic composite plates with free edges. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, vol. 21, iss. 1, pp. 26-34. DOI: 10.18500/1816-9791-2021-21-1-26-34, EDN: SFIPOI
The flexural strength of anisotropic composite plates with free edges
Modern technology shows increased demands on the strength properties of machines, their parts, as well as various structures, reducing their weight, volume and size, which leads to the need to use anisotropic composite materials. Finding criteria to determine the ultimate strength characteristics of structural elements, engineering structures is one of the urgent problems of solid mechanics. Strength problems in structures are often reduced to finding out the nature of the local stress state at the vertices of the joints of the constituent parts. The solution of this urgent problem for composite anisotropic plates can be found in this article, where the author continues the research in this area, extending them to the bending of anisotropic composite plates. The aim of the work is to study the limit stress state of anisotropic composite plates in the framework of the classical theory of plate bending. The outer edges of the plate are considered to be free. Using the classical theory of anisotropic plate bending in the space of physical and geometric parameters, the hypersurface equations determining the low-stress zones for the edge of the contact surface of a composite cylindrical orthotropic plate are obtained. Modern technological processes of welding, surfacing, soldering and bonding allow to produce structural elements of monolithic interconnected dissimilar anisotropic materials. The combination of different materials with qualities corresponding to certain operating conditions opens up great opportunities to improve the technical and economic characteristics of machines, equipment and structures. It can contribute to a significant increase in their reliability, durability, reduce the cost of production and operation. On this basis, the solution proposed in this work can be useful to increase the strength of composite materials.
- Chobanyan K. S. Napriazheniia v sostavnykh uprugikh telakh [Stresses in Compound Elastic Bodies]. Yerevan, Izd-vo AN Armianskoi SSR, 1987. 338 p. (in Russian).
- Zadoyan M. A. Low-stress conditions in composite plates. Doklady Akademii Nauk, 1993, vol. 332, no. 3, pp. 319–321 (in Russian).
- Akopyan A. G. Low-stress state in an inhomogeneous compound wedge with mixed boundary conditions. Journal of Applied Mechanics and Technical Physics, 1994, vol. 35, pp. 459–466. https://doi.org/10.1007/BF02369888
- Hakobyan A. G. On the plane deformation of a low-stress level nonhomogeneous-compound wedge. Mechanics. Proceedings of National Academy of Sciences of Armenia, 1994, vol. 47, iss. 5–6, pp. 42–48 (in Russian).
- Akopyan A. G., Zadoyan M. A. Low tension inhomogeneous composite wedges. Izvestia: Mechanics of Solids, 1992, no. 5, pp. 88–96 (in Russian).
- Lehnitsky S. G. Anizotropnye plastinki [Anisotropic Plates]. Moscow, Gostekhizdat, 1957. 463 p. (in Russian).
- Chyanbin Hwu. Anisotropic Elastic Plates. Springer Science & Business Media, 2010. 673 p.
- Williams M. L. Surface stress singularities resulting from various boundary conditions in angular corners of plates under bending. Proceedings of the First U. S. National Congress of Applied Mechanics, 1950, pp. 325–329.
- Burton W. S., Sinclair G. B. On the singularities in Reissner’s Theory for the bending of elastic plates. Journal of Applied Mechanics, 1986, vol. 53, no. 1, pp. 220–222.
- Gevorkyan G. V., Zadoyan M. A., Saakyan G. R., Sarkisyan S. M. Experimental study of the strength of composite plates in bending. Journal of Applied Mechanics and Technical Physics, 2000, vol. 41, iss. 4, pp. 763–767. https://doi.org/10.1007/BF02466879
- Zadoyan M. A. On the bond strength of a composite plate. Proceedings of National Academy of Sciences of Armenia and GIUA, Technical Sciences, 2000, vol. 53, no. 1, pp. 8–11 (in Russian).
- Akopyan A. G. On joint efficiency of composite anisotropic plate rigidly fixed along outside edges. Vestnik of Don State Technical University, 2019, vol. 19, no. 4, pp. 304–309. https://doi.org/10.23947/1992-5980-2019-19-4-304-309
- Akopyan A. G. Low-stress state of simply-supported anisotropic composite plates. Journal of Applied Mechanics and Technical Physics, 2019, vol. 60, iss. 4, pp. 692–697. https://doi.org/10.1134/S0021894419040138
- Nedorezov P. F. Numerical study of stress-strain state of a thin anisotropic rectangular plate. Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2009, vol. 9, iss. 4, pt. 2, pp. 143–148 (in Russian). https://doi.org/10.18500/1816-9791-2009-9-4-2-143-148
- Nedorezov P. F., Arystanbekova A. V. Static bending and vibrations of multilayer orthotropic rectangular plate with simply supported edges. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, 2011, iss. 1 (22), pp. 244–254 (in Russian). https://doi.org/10.14498/vsgtu926
- Kaloerov S. A., Zanko A. I. Bending of multiconnected anisotropic plates with the curvilinear holes. Izvestiya of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 4, pp. 456–464 (in Russian). https://doi.org/10.18500/1816-9791-2016-16-4-456-464
- Vijayakumar K. A relook at Reissner’s theory of plates in bending. Archive of Applied Mechanics, 2011, vol. 81, iss. 11, pp. 1717–1724. https://doi.org/10.1007/s00419-011-0513-4
- Vijayakumar K. Modified Kirchhoff’s theory of plates including transverse shear deformations. Mechanics Research Communications, 2011, vol. 38, iss. 3, pp. 211–213. https://doi.org/10.1016/j.mechrescom.2011.02.007
- Donnell L. G. Balki, plastiny i obolochki [Beams, Plates and Shells]. Moscow, Nauka, 1982. 568 p. (in Russian).
- Ambartsumyan S. A. Teoriya anizotropnykh plastin [Theory of Anisotropic Plates]. Moscow, Nauka, 1967. 360 p. (in Russian).
- 1861 reads