Stability of structural elements of special lifting mechanisms in the form of circular arches
DOI:
https://doi.org/10.15587/1729-4061.2018.125490Keywords:
stability problems, system of differential equations with variable coefficients, fundamental functions, BEMAbstract
The system of differential equations of stability of circular arches with symmetric sections and the sixth-order resolving ordinary differential equation are derived. It is noted that these equations have variable coefficients and their analytical solution under existing external loads leads to serious mathematical difficulties. The problem of finding exact solutions can be substantially simplified if we use the numerical-analytical version of the boundary element method (BEM). Here it is necessary to have a solution of the resolving equation of the problem, but with constant coefficients. This problem is much simpler than the initial one and can be realized according to the known procedure for constructing the fundamental functions of an ordinary differential equation. In this regard, the constants for integrating the general solutions of the differential equation are determined for the two most common cases and rationing of the fundamental functions in the matrix resolving form is performed. Recommendations are given on the solution of various boundary-value problems of stability of the simple bending of arch elements of special lifting mechanisms using them.
References
- De Backer, H., Outtier, A., Van Bogaert, P. (2014). Buckling design of steel tied-arch bridges. Journal of Constructional Steel Research, 103, 159–167. doi: 10.1016/j.jcsr.2014.09.004
- Louise, C. N., Md Othuman, A. M., Ramli, M. (2012). Performance of lightweight thin-walled steel sections: theoretical and mathematical considerations. Advances in Applied Science Research, 3 (5), 2847–2859.
- Pi, Y.-L., Bradford, M. A. (2013). In-plane stability of preloaded shallow arches against dynamic snap-through accounting for rotational end restraints. Engineering Structures, 56, 1496–1510. doi: 10.1016/j.engstruct.2013.07.020
- Becque, J., Lecce, M., Rasmussen, K. J. R. (2008). The direct strength method for stainless steel compression members. Journal of Constructional Steel Research, 64 (11), 1231–1238. doi: 10.1016/j.jcsr.2008.07.007
- Andreew, V. I., Chepurnenko, A. S., Yazyev, B. M. (2014). Energy Method in the Calculation Stability of Compressed Polymer Rods Considering Creep. Advanced Materials Research, 1004-1005, 257–260. doi: 10.4028/www.scientific.net/amr.1004-1005.257
- Artyukhin, Yu. P. (2012). Approximate analytical method for studying deformations of spatial curvilinear bars. Uchenye zapiski Kazanskogo Universiteta. Physics and mathematics, 154, 97–111.
- Qiu, W.-L., Kao, C.-S., Kou, C.-H., Tsai, J.-L., Yang, G. (2010). Stability Analysis of Special-Shape Arch Bridge. Tamkang Journal of Science and Engineering, 13 (4), 365–373.
- Pettit, J. R., Walker, A. E., Lowe, M. J. S. (2015). Improved detection of rough defects for ultrasonic nondestructive evaluation inspections based on finite element modeling of elastic wave scattering. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 62 (10), 1797–1808. doi: 10.1109/tuffc.2015.007140
- Langer U., Schanz M., Steinbach O., Wendland W. L. (Eds.) (2012). Fast Boundary Element Methods in Engineering and Industrial Applications. Lecture Notes in Applied and Computational Mechanics. Springer. doi: 10.1007/978-3-642-25670-7
- Orobey, V., Kolomiets, L., Lymarenko, A. (2015). Boundary element method in problem of plate elements bending of engineering structures. Metallurgical and Mining Industry, 4, 295–302.
- Kolomiets, L., Orobey, V., Lymarenko, A. (2016). Method of boundary elements in problems of stability of plane bending of rectangular section beams. Metallurgical and Mining Industry, 3, 58–65.
- Orobey, V., Daschenko, O., Kolomiets, L., Lymarenko, O., Ovcharov, Y. (2017). Mathematical modeling of the stressed-deformed state of circular arches of specialized cranes. Eastern-European Journal of Enterprise Technologies, 5 (7 (89)), 4–10. doi: 10.15587/1729-4061.2017.109649
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2018 Viktor Orobey, Oleksandr Daschenko, Leonid Kolomiets, Oleksandr Lymarenko
This work is licensed under a Creative Commons Attribution 4.0 International License.
The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.
A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.
