Approximate Analytical Solution for a Unilateral Contact Problem with Heavy Elastica
- Authors: Solyaev Y.1, Ustenko A.1, Lykosova E.1
-
Affiliations:
- Institute of Applied Mechanics of the Russian Academy of Sciences
- Issue: Vol 40, No 7 (2019)
- Pages: 1010-1015
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/205106
- DOI: https://doi.org/10.1134/S1995080219070163
- ID: 205106
Cite item
Abstract
The non-linear bending of slender heavy beam resting on rigid plane and subjected to the end point force is studied. Solution of the problem is derived by using series expansion technique. Approximate closed-form analytical solution for the length of the separated segment of elastica is found. It is shown that obtained simple solution can be used as the approximate lower bound for the evaluation of the force that should be applied to the beam’s end to provide the prescribed length of separation, while the known classical solution of linear theory can be used as the upper bound.
About the authors
Yu. Solyaev
Institute of Applied Mechanics of the Russian Academy of Sciences
Author for correspondence.
Email: yos@iam.ras.ru
Russian Federation, Moscow, 125040
A. Ustenko
Institute of Applied Mechanics of the Russian Academy of Sciences
Author for correspondence.
Email: audlord@yandex.ru
Russian Federation, Moscow, 125040
E. Lykosova
Institute of Applied Mechanics of the Russian Academy of Sciences
Author for correspondence.
Email: elykosova@mail.ru
Russian Federation, Moscow, 125040