Circular pressurized bulge

As noted above, the assumed deformation on which (5.87) is based is not kinematically admissible. An estimate of membrane response of the circular pressurized bulge which is, in fact, kinematically admissible can be obtained with only slightly more effort by appeal to energy arguments. To illustrate the approach, assume a two-parameter, axially symmetric deformation field for the bulge of the form... 

Fig. 5.34. The elastic energy release rate for axially symmetric expansion of the circular pressurized bulge. The energy release rate is normalized by the corresponding result for bending deformation only defined in (5.82) and pressure is normalized by the reference pressure defined in (5.81).

Circular pressurized bulge level of applied pressure is approximately... 

We start by describing an important phenomenon If in equilibrium a liquid surface is curved, there is a pressure difference across it. To illustrate this let us consider a circular part of the surface. The surface tension tends to minimize the area. This results in a planar geometry of the surface. In order to curve the surface, the pressure on one side must be larger than on the other side. The situation is much like that of a rubber membrane. If we, for instance, take a tube and close one end with a rubber membrane, the membrane will be planar (provided the membrane is under some tension) (Fig. 2.4). It will remain planar as long as the tube is open at the other end and the pressure inside the tube is equal to the outside pressure. If we now blow carefully into the tube, the membrane bulges out and becomes curved due to the increased pressure inside the tube. If we suck on the tube, the membrane bulges inside the tube because now the outside pressure is higher than the pressure inside the tube. 

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