The use of cubic splines in the modeling of creep processes of linear viscoelastic materials under complex stress state

Authors

  • V. S. Ushakova S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv
  • O. V. Ushakov Ukrainian scientific and research Institute of special equipment and forensic expertise of the Security Service of Ukraine, Kyiv
  • O. Y. Gorun Ukrainian scientific and research Institute of special equipment and forensic expertise of the Security Service of Ukraine, Kyiv

DOI:

https://doi.org/10.17721/1812-5409.2023/2.27

Keywords:

linear viscoelasticity, complex stress state, spline approximation, creep function, hereditarty kernels, quadratic deviation, quantile of statistics

Abstract

The processes of creep of thin-walled tubular elements made of linear viscoelastic materials under complex stress conditions are considered. The discrete values of basic experimental data on uniaxial tension and pure torsion are considered. These discrete values are used for identification of hereditary kernels normally used in creep modeling processes under complex stress conditions. As an example material, plexiglass ST1 is used for calculations. The area of linearity of the model is substantiated by the value of the quantile of statistics and the hypothesis of the existence of a unified creep function in a certain, predetermined confidence interval. The creep function is invariant with respect to stresses and is built with making use of the yield curves. Constitutive equations of the model contain a set of functions and coefficients determined from basic experiments. For further calculations, the experimental data are approximated by a power function followed by the smoothing with cubic splines. Approximation analysis is carried out by evaluation of the least squared deviation of experimental data from the calculated data. The approximating function is analyzed with making use of minimum of the quadratic deviation.

Pages of the article in the issue: 156 - 159

Language of the article: Ukrainian

References

RABOTNOV, U.N. (1966) Polzuchest` elementov konstrukcii. Moskva: Nauka.

KRISTENSEN, R.M. (1974). Vvedenie v teoriu vyazkouprugosti. Moskva: Mir.

GOLUB,V.P., KOBZAR,U.M., RAGULINA, V.S. (2013) K zadache opredeleniya parametrov yader nasledstvennosti izotropnih nelineyno-vyazkouprugih materialov pri slognom napryagennom sostoyanii. Teoret. i prikl. mehanika. 5(51). p. 26-35.

GOLUB, V.P., KOBZAR, U.M., FERNATI,P.V. (2014). K resheniu zadach polzuchesti izotropnih nelineyno-vyazkouprugih materialov pri slognom napryagennom sostoyanii. Teoret. i prikl. mehanika. 8(54). p. 45-56.

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Published

2023-12-23

How to Cite

Ushakova, V. S., Ushakov, O. V., & Gorun, O. Y. (2023). The use of cubic splines in the modeling of creep processes of linear viscoelastic materials under complex stress state. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 156–159. https://doi.org/10.17721/1812-5409.2023/2.27

Issue

Section

Differential equations, mathematical physics and mechanics