PHYSICAL AND MECHANICAL STATE OF CANTILEVER TRIANGULAR PLATES
DOI:
https://doi.org/10.26577/JMMCS.2023.v118.i2.07Keywords:
triangular plate, numerical method, grid method,, deflection, bending stiffness, rod analogy, reduction factorAbstract
In this paper, the bending of cantilever triangular plates at the same angles of inclination of the side edges to the base is investigated. Due to the complexity of the boundary conditions, a numerical finite difference method is applied using a grid of scalene triangles that fits well into the contour of the plate. To solve the problem of an acute angle at the top of the plate, the method of combining the results of calculating a cantilever bar of variable bending stiffness with similar results of calculating a triangular plate supported along the contour using a reduction factor is applied. The results of deflections of the cantilever triangular plate at different angles of inclination of the side edges to the base are given. The theoretical provisions and applied results of this study can be used both in scientific research and in engineering design.
References
[1] Bosakov S.V., Skachek P.D. Static calculation of triangular plates with hinged sides. Mechanics. Research and innovation, 2017, No. 10, pp. 24 - 28.
[2] Akhmediev S.K., Zhakibekov M.E., Kurokhtina I.N. Nuguzhinov Zh.S. NNumerical study of the stress-strain state of structures such as thin triangular plates and plates of medium thickness. Structural mechanics and calculation of structures, 2015, No. 2 (259), pp. 28 - 33.
[3] Bosakov S.V., Skachek P.D. Application of the Ritz method in the calculations of triangular plates with different conditions of fastening to the action of a static load. Structural mechanics and calculation of structures, 2018, No. 5 (280), pp. 17 - 23.
[4] Korobko A.V., Kalashnikova N.G., Abashin E.G. Transverse bending and free vibrations of elastic isotropic plates in the form of isosceles triangles. Construction and reconstruction, 2021, No. 6, pp. 20 - 27. https://doi.org/10.33979/2073-7416- 2021-98-6-20-27
[5] Korobko A.V., Chernyaev A.A., Shlyakhov S.V. Application of the MICF method for calculating triangular and quadrangular plates using widely known geometric parameters. Construction and reconstruction, 2016, No. 4, pp. 19 - 28.
[6] Saliba H.T. Triangular elements and the superposition techniques in till free vibration analysis of plates. Mecanique industrielle et materiaux (11th Colloquium on Vibrations, Shocks and Noise), 1996, No. 49 (4), pp. 168 - 170.
[7] Korobko A.V. Calculation of triangular plates by interpolation method by the shape coefficient using affine
transformations. News of higher educational institutions. Aviation technology, 2003, No. 2, pp. 13 - 16.
[8] Korobko V.I., Savin S.Yu. Free vibrations of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and reconstruction, 2013, No. 2, pp. 33 - 40.
[9] Korobko V.I., Savin S.Yu., Boyarkina S.V. Bending of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and Reconstruction, 2012, No. 1, pp. 7 - 13.
[10] Muromsky A.S., Korobko A.V. Calculation of triangular plates using affine transformations. Proceedings of the 55th International scientific and technical conference of young scientists (doctoral students, postgraduates and students) "Actual problems of modern construction St. Petersburg, 2001.
[11] Vlasov V.I., Gorshkov A.B., Kovalev R.V., Lunev V.V. Thin triangular plate with a blunted vertex in a viscous hypersonic flow. 2009, No. 4, pp. 134 - 145.
[12] Grigorenko O.Y., Borisenko M.Y., Boichuk O.V. et al. Free vibrations of triangular plates with a hole*. Int Appl Mech., 2021, No. 57, pр. 534 - 542. https://doi.org/10.1007/s10778-021-01104-3.
[13] Dongze He, Tao Liu, Bin Qin, Qingshan Wang, Zhanyu Zhai, Dongyan Shi. In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach. Composite Structures, 2021. DOI: 10.1016/j.compstruct.2021.114138.
[14] Iman Dayyani, Masih Moore, Alireza Shahidi. Unilateral buckling of point-restrained triangular plates. Thin-Walled Structures, 2013, Vol. 66, pр 1 - 8.
[15] Cai D., Wang X., Zhou G. Static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports, Thin-Walled Structures, 2021, Vol. 162, No. 107592.
[16] Varvak P.M., Varvak L.P. Method of grids in problems of calculation for building structures. Moscow, Stroyizdat, 1977, 154 p.
[17] Karamansky T.D. Numerical methods of structural mechanics. Moscow, Stroyizdat, 1980, 434 p.
[18] Akhmediev S.K. Analytical and numerical methods for calculating machine-building and transport constructions and structures (textbook). Karaganda, KarTU, 2016, 158 p.
[19] Akhmediev S.K. Calculations of triangular plates. Karaganda, KarTU, 2006, 86 p.
[20] Nuguzhinov Z.S., Akhmediyev S.K., Donenbayev B.S., Kurokhtin A.Yu., Khabidolda O. Comparative analysis of designing wall panels with hole based on one-dimensional and two-dimensional computer models. IOP Conf. Series: Materials Science and Engineering, 2018, 456 012082. DOI:10.1088/1757-899X/456/1/012082
[21] Kasimov A.T., Yessenbayeva G.A., Zholmagambetov S.R., Khabidolda O. Investigation of layered orthotropic structures based on one modified refined bending theory. Eurasian Physical Technical Journal, 2021, Vol.18, No. 4(38), pp. 37 - 44. DOI 10.31489/2021No4/37-44
[2] Akhmediev S.K., Zhakibekov M.E., Kurokhtina I.N. Nuguzhinov Zh.S. NNumerical study of the stress-strain state of structures such as thin triangular plates and plates of medium thickness. Structural mechanics and calculation of structures, 2015, No. 2 (259), pp. 28 - 33.
[3] Bosakov S.V., Skachek P.D. Application of the Ritz method in the calculations of triangular plates with different conditions of fastening to the action of a static load. Structural mechanics and calculation of structures, 2018, No. 5 (280), pp. 17 - 23.
[4] Korobko A.V., Kalashnikova N.G., Abashin E.G. Transverse bending and free vibrations of elastic isotropic plates in the form of isosceles triangles. Construction and reconstruction, 2021, No. 6, pp. 20 - 27. https://doi.org/10.33979/2073-7416- 2021-98-6-20-27
[5] Korobko A.V., Chernyaev A.A., Shlyakhov S.V. Application of the MICF method for calculating triangular and quadrangular plates using widely known geometric parameters. Construction and reconstruction, 2016, No. 4, pp. 19 - 28.
[6] Saliba H.T. Triangular elements and the superposition techniques in till free vibration analysis of plates. Mecanique industrielle et materiaux (11th Colloquium on Vibrations, Shocks and Noise), 1996, No. 49 (4), pp. 168 - 170.
[7] Korobko A.V. Calculation of triangular plates by interpolation method by the shape coefficient using affine
transformations. News of higher educational institutions. Aviation technology, 2003, No. 2, pp. 13 - 16.
[8] Korobko V.I., Savin S.Yu. Free vibrations of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and reconstruction, 2013, No. 2, pp. 33 - 40.
[9] Korobko V.I., Savin S.Yu., Boyarkina S.V. Bending of triangular orthotropic plates with homogeneous and combined boundary conditions. Construction and Reconstruction, 2012, No. 1, pp. 7 - 13.
[10] Muromsky A.S., Korobko A.V. Calculation of triangular plates using affine transformations. Proceedings of the 55th International scientific and technical conference of young scientists (doctoral students, postgraduates and students) "Actual problems of modern construction St. Petersburg, 2001.
[11] Vlasov V.I., Gorshkov A.B., Kovalev R.V., Lunev V.V. Thin triangular plate with a blunted vertex in a viscous hypersonic flow. 2009, No. 4, pp. 134 - 145.
[12] Grigorenko O.Y., Borisenko M.Y., Boichuk O.V. et al. Free vibrations of triangular plates with a hole*. Int Appl Mech., 2021, No. 57, pр. 534 - 542. https://doi.org/10.1007/s10778-021-01104-3.
[13] Dongze He, Tao Liu, Bin Qin, Qingshan Wang, Zhanyu Zhai, Dongyan Shi. In-plane modal studies of arbitrary laminated triangular plates with elastic boundary constraints by the Chebyshev-Ritz approach. Composite Structures, 2021. DOI: 10.1016/j.compstruct.2021.114138.
[14] Iman Dayyani, Masih Moore, Alireza Shahidi. Unilateral buckling of point-restrained triangular plates. Thin-Walled Structures, 2013, Vol. 66, pр 1 - 8.
[15] Cai D., Wang X., Zhou G. Static and free vibration analysis of thin arbitrary-shaped triangular plates under various boundary and internal supports, Thin-Walled Structures, 2021, Vol. 162, No. 107592.
[16] Varvak P.M., Varvak L.P. Method of grids in problems of calculation for building structures. Moscow, Stroyizdat, 1977, 154 p.
[17] Karamansky T.D. Numerical methods of structural mechanics. Moscow, Stroyizdat, 1980, 434 p.
[18] Akhmediev S.K. Analytical and numerical methods for calculating machine-building and transport constructions and structures (textbook). Karaganda, KarTU, 2016, 158 p.
[19] Akhmediev S.K. Calculations of triangular plates. Karaganda, KarTU, 2006, 86 p.
[20] Nuguzhinov Z.S., Akhmediyev S.K., Donenbayev B.S., Kurokhtin A.Yu., Khabidolda O. Comparative analysis of designing wall panels with hole based on one-dimensional and two-dimensional computer models. IOP Conf. Series: Materials Science and Engineering, 2018, 456 012082. DOI:10.1088/1757-899X/456/1/012082
[21] Kasimov A.T., Yessenbayeva G.A., Zholmagambetov S.R., Khabidolda O. Investigation of layered orthotropic structures based on one modified refined bending theory. Eurasian Physical Technical Journal, 2021, Vol.18, No. 4(38), pp. 37 - 44. DOI 10.31489/2021No4/37-44
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Published
2023-07-01
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Section
Mechanics
