Vol.2, No 1, 1999 pp. 15-21
UDC 514.772.35(045)

ANALYSIS OF BENDING OF SURFACES
USING PROGRAM PACKAGE MATHEMATICA
Ljubica S. Velimirović
Faculty of Science, Department of Mathematics, University of Niš
Ćirila i Metodija 2, 18000 Niš, Yugoslavia
E-mail: vljubica@archimed.filfak.ni.ac.yu

Abstract. In this paper we consider surface bending using program package Mathematica. Bending and infinitesimal bending of surfaces are considered. Infinitesimal bending of rotational surfaces is considered using Cohn-Vossen's method. The results obtained by solving differential equations are presented graphically.
As an example of non-rigid surfaces Belov's surface is pointed out. Belov's non-rigid toroid is drawn at Mathematica. The surface that is infinitesimal bending of the Belov's toroid is also given. Field of infinitesimal bending for this surface is also considered. The joint circles generated by the apices of Belov's quadrangle, deformed to the curves that are not circles are also given.
Key words: bending, infinitesimal bending, infinitesimal bending field, toroid

ANALIZA SAVIJANJA POVRŠI UZ KORIŠĆENJE PROGRAMSKOG PAKETA MATHEMATICA
U radu se razmatra savijanje površi uz korišćenje programskog paketa Mathematica. Predstavljen je poznati primer savijanja katenoida do helikoida . U radu se razmatra beskonačno malo savijanje rotacionih površi uz korišćenje metoda Kon-Fosena. Rezultat dobijen rešavanjem diferencijalnih jednačina prikazan je grafički.
Specijalno, nacrtan je primer nekrutog toroida Belova . Polje savijanja dato je grafički, a takodje i deformisani toroid,kako po delovima, tako i u celini. Krugovi spajanja koji su generisani temenima Belovljevog četvorougla deformisani u krive koje nisu krugovi su takodje dati.
Ključne reči: savijanje, beskonačno malo savijanje, toroid, polje beskonačno malog savijanja