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Analytical Method of Calculating Beams of Variable Stiffness on an Elastic Winkler Base

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Abstract:

The problem of bending of a beam of variable stiffness resting on a continuous homogeneous elastic Winkler-type foundation is considered. The exact solution of the corresponding bending differential equation is found for the case when the beam stiffness is an arbitrary continuous function. Based on the exact solution, an analytical method for beam calculation is developed. This method produces accurate results and is computationally efficient. It is implemented in a computer program and demonstrated by the calculation of a truncated wedge-shaped beam. The calculation results are provided in numerical and graphical formats.

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Periodical:

Advances in Science and Technology (Volume 170)

Pages:

37-51

DOI:

https://doi.org/10.4028/p-SnX543

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Online since:

November 2025

Authors:

Yurii Krutii, Mykola Surianinov*, Dina Lazarieva, Alla Perperi, Vladyslav Vakulenko

Keywords:

Analytical Method, Beam, Bending Equation, Exact Solution, Variable Stiffness, Winkler Hypothesis

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© 2025 Trans Tech Publications Ltd. All Rights Reserved

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References

[1] S.P. Timoshenko, A Course in Elasticity Theory [in Russian]. Naukova Dumka, Kiev, 1972.

Google Scholar

[2] Yu. Krutii, M. Surianinov, S. Petrash, M. Yezhov, Development of an analytical method for calculating beams on a variable elastic Winkler foundation. IOP Conference Series: Materials Science and Engineering. 1162(1) (2021) 012009

DOI: 10.1088/1757-899X/1162/1/012009

Google Scholar

[3] Y. Krutii, M. Surianinov, V. Vakulenko, M. Soroka, N. Vasilieva, Analytical Calculation of Beams on Winkler's Variable Elastic Foundation. Advances in Science and Technology. 156 (2024) 75–80

DOI: 10.4028/p-PD9h3g

Google Scholar

[4] D. Cao, B. Wang, W. Hu, Y. Gao, Free Vibration of Axially Functionally Graded Beam. Mechanics of Functionally Graded Materials and Structures. IntechOpen, 2020

DOI: 10.5772/intechopen.85835

Google Scholar

[5] T.S. Jang, A general method for analyzing moderately large deflections of a non-uniform beam: An infinite Bernoulli-Euler-von Karman beam on a nonlinear elastic foundation. Acta Mechanica. 225 (2014.) 1967–1984

DOI: 10.1007/s00707-013-1077-x

Google Scholar

[6] T.S. Jang, H.G. Sung, A new semi-analytical method for the non-linear static analysis of an infinite beam on a non-linear elastic foundation: a general approach to a variable beam cross-section. International Journal of Non-Linear Mechanics. 47 (2012) 132–139

DOI: 10.1016/j.ijnonlinmec.2012.04.005

Google Scholar

[7] G.C. Tsiatas, Nonlinear analysis of non-uniform beams on nonlinear elastic foundation. Acta Mechanica. 209 (2010) 141–152

DOI: 10.1007/s00707-009-0174-3

Google Scholar

[8] A.M. Poliakov, P.K. Shtanko, V.I. Pakhaliuk, Calculation of a variable cross-section beam on an elastic foundation with two coefficients of compliance. Journal of Physics: Conference Series. 1353 (2019) 012110

DOI: 10.1088/1742-6596/1353/1/012110

Google Scholar

[9] P. Deminov, The stiffness of a reinforced concrete beam with random parameters the cracks formation. E3S Web of Conferences. 410 (2023) 02025. https://doi.org/10.1051/e3sconf/ 202341002025

DOI: 10.1051/e3sconf/202341002025

Google Scholar

[10] U. Mutman, Free vibration analysis of an Euler beam of variable width on the Winkler foundation using homotopy perturbation method. Mathematical Problems in Engineering. 1–9 (2013)

DOI: 10.1155/2013/721294

Google Scholar

[11] S. Akhmediev, V. Mikhailov, G. Tazhenova, M. Bakirov, T. Filippova, D. Tokanov, Calculating a beam of variable section lying on an elastic foundation. Journal of Applied Engineering Sciences. 21(1) (2023) 87–93

DOI: 10.5937/jaes0-38800

Google Scholar

[12] M. Nikodým, K. Frydrýšek. About central difference method applied for the beams on elastic foundation. Transactions of the VŠB-Technical University of Ostrava, Mechanical Series. 2 (2013) 133-146

DOI: 10.22223/tr.2013-2/1967

Google Scholar

[13] Y.S. Krutii, Development of a method for solving problems of stability and vibrations of deformable systems with variable continuous parameters [in Ukrainian]. Sc.D. diss., Odesa, 2016.

Google Scholar

[14] Y.S. Krutii, Construction of a solution of the problem of stability of a bar with arbitrary continuous parameters. Journal of Mathematical Sciences. 231 (2018) 665–677

DOI: 10.1007/s10958-018-3843-8

Google Scholar

[15] V.I. Shvab'yuk, Y.S. Krutii, M.G. Sur'yaninov, Investigation of the Free Vibrations of Bar Elements with Variable Parameters Using the Direct Integration Method. Strength of Materials. 48 (2016) 384–393

DOI: 10.1007/s11223-016-9776-x

Google Scholar

[16] Y.S. Krutii, M.G. Sur'yaninov, G.S. Karnaukhova, Calculation Method for Axisymmetric Bending of Circular and Annular Plates on a Changeable Elastic Bed. Part 1. Analytical Relations. Strength of Materials. 53(2) (2021) 247–257

DOI: 10.1007/s11223-021-00282-2

Google Scholar

[17] F.R. Gantmacher, The Theory of Matrices. Chelsea, New York, 1959.

Google Scholar