Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Circularly symmetric deformation of shallow elastic membrane caps


Author: Kurt N. Johnson
Journal: Quart. Appl. Math. 55 (1997), 537-550
MSC: Primary 73K10; Secondary 34B15
DOI: https://doi.org/10.1090/qam/1466147
MathSciNet review: MR1466147
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider shallow elastic membrane caps that are rotationally symmetric in their undeformed state, and investigate their deformation under small uniform vertical pressure and a given boundary stress or boundary displacement. To do this we use the small-strain theory developed by Bromberg and Stoker, Reissner, and Dickey. We deal with the two-parameter family of membranes whose undeformed configuration is given in cylindrical coordinates as

$\displaystyle z\left( x \right) = C\left( {1 - {x^\gamma }} \right), \qquad \left( 1 \right)$

which includes the spherical cap as a special case ( $ \gamma = 2$ and $ C$ small). We show that if $ \gamma > 4/3$ then a circularly symmetric deformation is possible for any positive boundary stress (or any boundary displacement) and any positive pressure, but if $ 1 < \gamma < 4/3$ then no circularly symmetric deformation is possible if the stress and pressure are positive and small (or for non-positive boundary displacement and small positive pressure).

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73K10, 34B15

Retrieve articles in all journals with MSC: 73K10, 34B15


Additional Information

DOI: https://doi.org/10.1090/qam/1466147
Article copyright: © Copyright 1997 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website