Results are reported for the axisymmetric response of an initially flat annular membrane to transverse deflections of a rigid inclusion centered within the membrane. The membrane material is assumed to behave elastically in accordance with the Mooney-Rivlin constitutive law. The response shows a dramatic change in features with variations in one of the two Mooney-Rivlin parameters. Corresponding to negative values of this parameter, the membrane wrinkles for sufficiently high loads, whereas for positive values and large enough loads, it assumes an hourglass profile without wrinkling. For the case when this parameter vanishes, in which case it is of the neo-Hookean type, the load may be increased indefinitely without causing the membrane to wrinkle or go into an hourglass profile. The non-linear system of first-order differential equations governing the problem is solved by a predictor/multi-corrector integration method.
ASJC Scopus subject areas
- Mechanical Engineering
- Statistical and Nonlinear Physics