The use of cubic splines in the modeling of creep processes of linear viscoelastic materials under complex stress state
DOI:
https://doi.org/10.17721/1812-5409.2023/2.27Keywords:
linear viscoelasticity, complex stress state, spline approximation, creep function, hereditarty kernels, quadratic deviation, quantile of statisticsAbstract
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.
Downloads
Published
Issue
Section
License
Copyright (c) 2023 V. S. Ushakova, O. V. Ushakov, O. Y. Gorun
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
