Mathematical modeling of the stressed-deformed state of circular arches of specialized cranes
DOI:
https://doi.org/10.15587/1729-4061.2017.109649Keywords:
boundary element method, fundamental system of functions, arched systems, specialized crane, MATLABAbstract
We present the possibilities to calculate the stressed-deformed state of circular arches under various conditions of bearing based on the algorithm of a numerical-analytical variant of the method of boundary elements and application of the MATLAB programming and calculation environment. The exact solution to the problem of flat deformation of a circular rod is shown, considering the deformations of bending and stretching-compression, which has not so far been implemented in professional packages of the finite element method. We have constructed solving equations for the boundary value problems on flat deformation of circular arches under various bearing conditions. An example is given for calculating the circular arch SDS employing BEM; by using the MATLAB environment, we represented the results numerically and visually in the form of diagrams. It was established that the boundary element method in the calculation of circular arches has the simplest algorithm logic among other methods and it allows obtaining accurate and reliable results of the stressed-deformed state of crane structures with specialized designation. BEM presented in the given work could be successfully applied to solving boundary value problems for differential equations with variable coefficients. The structure in this case should be discretized while the BEM algorithm does not change. Additional advantage is the minimal requirements to variable coefficients of the differential equation. They may possess first-order discontinuities, breakpoints, and an arbitrary set of continuous functions, which significantly expands the range of problems to be solved.
It is obvious that the boundary element method enables fulfillment of the increased requirements to calculation results, which therefore renders relevance to the present study, as well as scientific and practical value for professionals involved in the design of crane structuresReferences
- 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. (2012). Fast Boundary Element Methods in Engineering and Industrial Applications. Springer. doi: 10.1007/978-3-642-25670-7
- Orobej, V., Kolomiets, L., Lymarenko, A. (2015). Metallurgical and Mining Industry, 4, 295–302.
- Kolomiets, L., Orobey, V., Lymarenko, A. (2016). Metallurgical and Mining Industry, 3, 59–65.
- Gulyar, O. I., Piskunov, S. O., Shkril, O. O., Romantsova, K. S. (2015). Stiffness matrix and vector nodal reaction of circular finite element numerical integration. Resistance of Materials and Theory of Buildings, 95, 81–89.
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Copyright (c) 2017 Viktor Orobey, Oleksandr Daschenko, Leonid Kolomiets, Oleksandr Lymarenko, Yuri Ovcharov
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