Einige Anwendungen der Theorie der Zylinderschale

Abstract

Die Theorie der Zylinderschale wird auf die Berechnung nichtgeschlossener Teilstiicke erweitert fiir den Fall einer nur von einer Koordinate abhangigen Spannungsverteilung. Die Theorie wird dann auf die quergewolbte Biegefeder und die Bimetall-Zylinderfeder angewandt. Die genannte Biegefeder hat eine nichtlineare Charakteristik und wird bei Erreichen einer kritischen Durchbiegung instabil. I m iiberkritischen Bereich bleibt das Biegemoment annbhernd konstant und diese Eigenschaft wird zu9n hntrieb mechanischer Werke ausgenutzt.The theory of cylindrical shells is extended t o open divisions of this shellsforthe case of uniformstress distribution along one direction. This theory is then applied to the cross-curved leaf spring and the bimetallic cylinder spring. The fore-mentioned leaf spring has a nonlinear characleristic and when reaching a critical point becomes unstable. I n supercritical state the bending moment remains approximately constant and this quality is used for the construction of spring works. La thdorie des coques cylindriques est dtendue iC des parties non fermkes de celles-ci pour le cas d'une distribution uniforme des tensions dans une direction. Cette thborie est ensuite appliqute au ressort b lame de section courbte et a u ressort bimetallique eylindriforme. Le dit ressort b lame a une characteristique nonlindaire et en atteignant un &at critique devient instabil. En &at supercritique le moment est b peu prBs constant et cette qualitd est employb pour la construetion de mouvements 8. ressort. Teopm qmmqpnnecrco8 IIOJIOCTH pacnpocTpameTca ~a pacseT H e m m q T m w m e 8 na TOT caysat, rcorga pacnpegeneme Hanpaxema ~~B H C M T T O~K O OT o q~o t KoopgmaTba. ,@nee, Teopm n p m e m e w s K nonpenHo-sHnyEnoB npymme m3r~6a EI K 6 n~e~a n n~n e c~o B qHnmgpmecKofi npyxme. Y~O M R H~T~R npyxmia ~13r~16a 0 6 n a~a e~ nenmeBHofi xapamepmcm-KOB, H, A O C T H~H~B xpmmecreoro nporxba, cTanoBmcg He yc~oitsu~o8. B c s e p x~p m m e c~o t o 6 n a c~~ m3rn6a1011@4 MoMeHT @cTaeTcn I~~H~J I M X~H H O IIOCTORHHHM , BTO C B O~C T B O ~cnonb-3 y e~c s ~n s npmona M~X~H H S M O B . Zur Berechnung ringformig geschlossener Zylinder wird von B i e z e n o -G r a m m e 1 [l]

Extremely Deformable Structures

“…An analytical solution to this problem was found by Wuest (1954) together with other solutions for "cross-curved leaf springs." His solution was laterincluded in a Russian monograph, later translated into English, by Panovko and Gubanova (1965).…”

Folding Large Antenna Tape Spring

“…They were first studied by Wuest [5], who obtained an analytical expression for the moment-curvature relationship that allowed for changes in the transverse curvature. Their exploitation for deployable structures applications began with Rimrott's work, in the 1960s.…”

Analysis of tape spring hinges

“…In a pair, one tape is subjected to equal sense bending while the other is subjected to opposite sense bending during deployment and vice versa after postlatching. Behaviour of a metallic tape spring subject to the opposite sense bending was first studied by Wuest [1]. Later Mansfield studied large-deflection torsional and flexural behaviour of tape springs [2].…”

“…Starting from the unloaded, straight configuration, for opposite sense bending the tape behaves linearly up to a maximum moment, M max þ , then it snaps and behaves as a constant moment spring, carrying M Ã þ while it behaves linearly down to a minimum moment, M Ã À and again behaves as a constant moment spring, carrying M Ã À for equal sense bending. Opposite-sense moment versus curvature of a tape spring made of isotropic material was first obtained by Wuest [1]. Wuest obtained the moment-curvature relationship of a tape spring subject to equal and opposite end moments, considering a slightly distorted axi-symmetric cylindrical shell.…”