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
