CHAPTER 2
THEORETICAL DEVELOPMENT
The development of the theory applied to analytical solutions used in later chapters
is described in Chapter 2. A standard fluid flow analysis is first presented, followed by
the traditional beam method applied to inflatable theory, which is chosen from the
methods presented in Chapter 1. The theory presented focuses on inflated beams before
and at the point of wrinkling. The model used for derivation is an internally pressurized
circular-cylindrical closed-end fabric tube. The internal pressure acting over the surface
area of the end caps translates to pretension forces in the fabric tube. The essence of the
inflatable theory is that bending causes a compressive stress on the underside of the tube
opposing the tensile stress caused by the pretension forces. Wrinkling occurs when the
compressive portion of bending stress exceeds the pretension stress. In some cases, stress
resultant, c*, is used to replace axial stress, c, throughout the analysis, as described in
Main's theory, to more accurately model fabric behavior (Main et al., 1994). This also
leads to using a resultant elastic modulus, E*, with units of force per unit length.
2.1 Fluid Analysis
The fluid analysis is used to determine the total drag force acting on a cylinder for a
given external flow condition. The following assumptions are made for the fluid
analysis:
* Smooth cylinder surface
* Constant temperature fluid and material properties at 200C