 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| A.D. Chernyshov, V.V. Goryainov, and M.I. Popov, "Investigation of the Errors of Fast Trigonometric Interpolation in Solving the Problem of Stresses in a Bar," Mech. Solids. 58 (1), 95-107 (2023) |
| Year |
2023 |
Volume |
58 |
Number |
1 |
Pages |
95-107 |
| DOI |
10.3103/S0025654422700017 |
| Title |
Investigation of the Errors of Fast Trigonometric Interpolation in Solving the Problem of Stresses in a Bar |
| Author(s) |
A.D. Chernyshov (Voronezh State University of Engineering Technologies, Voronezh, 394036 Russia, chernyshovad@mail.ru)
V.V. Goryainov (Voronezh State Technical University, Voronezh, 394006 Russia, gorvit77@mail.ru)
M.I. Popov (Voronezh State University of Engineering Technologies, Voronezh, 394036 Russia, mihail_semilov@mail.ru) |
| Abstract |
Using the fast trigonometric interpolation, the problem on stresses in a rectangular bar is solved. The obtained approximate analytical solution is compared with the exact one. During this analysis the relative error of the displacement components, the stress tensor components, the discrepancy between the Lame equilibrium equations, and the discrepancy of the boundary conditions are investigated. It has been established that when using the second-order boundary function in fast expansions and a small number of terms in the Fourier series (from two to six), the maximum relative error δmath max of the displacement components and the stress tensor components is less than one percent. With an increase in the order of the boundary function and/or the number of terms N in the Fourier series, δmath decreases rapidly. Increasing the order of the boundary function is a more effective way to reduce the calculation error of δmath max than increasing the number of terms in the Fourier series. When studying the intensity of stresses σ in a bar with different overall dimensions of a rectangular cross-section, but with the same area of all sections, it has turned out that the smallest value of σmath all cross-sections is observed for a bar with a square section. |
| Keywords |
displacements, stress tensor components, Lame equations, fast expansions, fast trinometric interpolation, high accuracy |
| Received |
27 March 2022 | Revised |
24 April 2022 | Accepted |
25 April 2022 |
| Link to Fulltext |
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