R A Schachar et al 2008 J. Phys. A: Math. Theor. 41 495204 doi:10.1088/1751-8113/41/49/495204
R A Schachar1,6, G G Liao2, R D Kirby2, F Kamagar3, J H Savoie4, A Abolmaali4 and G Rosensteel5
Show affiliationsThe purpose of the study was to determine the change in shape of an encapsulated spheroid associated with an increase in its circumferential equatorial diameter. Using nonlinear finite element analysis the effects of changing the spheroid's aspect ratio, the elastic modulus of its capsule and the Poisson's ratio of the encapsulated fluid were assessed. We found that when the equatorial diameter of a spheroid with an aspect ratio of ≤0.6 was increased, the new central sagittal cross sectional profile of the oblate spheroid was no longer elliptical. The new profile had a larger minor axis, the curvature at its poles was steeper and the curvature near its equator was flatter than the original profile. The new profile referred to herein as a 'steep profile' also occurred when the major axis of a two-dimensional ellipse with an aspect ratio of ≤0.6 was increased providing the area enclosed by the ellipse was held constant or allowed to minimally decrease. 'Steep profiles' occur in encapsulated oblate spheroids with different material properties, in two-dimensional ellipses and floating oil films. This suggests that the phenomenon may have universal implications.
Issue 49 (12 December 2008)
Received 5 February 2008, in final form 5 August 2008
Published 29 October 2008
R A Schachar et al 2008 J. Phys. A: Math. Theor. 41 495204
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