COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER
Abstract
The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.
Downloads
Metrics
References
1. Zienkiewicz, O. (1975). The finite element method in engineering science. Moscow: Mir.
2. Zienkiewicz, O. & Chang, I. (1974). The finite element method in the theory of structures and the mechanics of a continuous medium. Moscow: Nedra.
3. Tolok, V.A., Kyrychevskyi, V.V., Gomeniuk, S.I., Hrebeniuk, S.N. & Buvailo, D.P. (2003). Finite element method: theory, algorithms, implementation. Kyiv: Naukova dumka.
4. Norrie, D. & Vriez, Zh. (1981). An Introduction to Finite Element Analysis. Moscow: Mir.
5. Segerlind, L. (1979). Applied Finite Element Analysis. Moscow: Mir.
6. Kamaeva, L. Y. & Khomchenko, A. N. (1988). Computational experiments with alternative bases serendipity approximations, Prykl. probl. prochnosty y plastychnosty. Analyz y optymyzatsyia deformyruemykh system. Vsesoiuz. mezhvuz. sb., 39, 103-105.
7. Kamaeva, L. Y. & Khomchenko, A. N. (1985). New finite element models of the Serendip family. Yvano-Frankovsk.
8. Khomchenko, A. N. & Kamaeva, L. Y. (1987). Geometric aspects of serendipity approximations. Yvano-Frankovsk.
9. Khomchenko, A. N. & Litvinenko, E. Y., Guchek, P. Y. (1996). Geometry of the Serendip Approximations. Prykl. heom. y ynzh. hrafyka, 59, 40-42.
10. Kamaeva, L. Y. & Khomchenko, A. N. (1985). On the modeling of finite elements of the Serendip family. Prykl. probl. prochnosty y plastychnosty. Alhorytmyzatsyia y avtomatyzatsyia reshenyia zadach upruhosty y plastychnosty. Vsesoiuz. mezhvuz. sb., 31, 14-17.
11. Khomchenko, A.N., Koval, N.V. & Osipova, N.V. (2016). Cognitive computer graphics as a means of "soft" modeling in problems of restoration of functions of two variables. Information Technologies in Education, 28, 7-18. DOI: 10.14308/ite000599.
12. Zienkiewicz, O. & Morgan, K. (1986). Finite Elements and Approximation. Moscow: Mir.
13. Strang, H. & Fix, Dzh. (1977). An Analysis of the Finite Element Method. Moscow: Mir.