deflection behavior. Experimental results agreed for aspect ratios of l/d>6 (Main et al.,
1994).
1.3.2 Nonlinear Approach
Since inflatable beams behave nonlinearly, a nonlinear approach, although
complex, is the most logical method. Douglas uses the theory of incremental
deformations to find the Cauchy-Green deformation tensors which can be related to
determine the Lagrangian and Eulerian Strains. These lead to a stress-deformation
relation. This is all then applied to an inflated beam incorporating the pressure in as a
stress. The variation in beam stiffness is plotted as a function of changing internal
pressure. Unlike a linear approach, this thorough method takes into account the changes
in geometry and changes in material properties (Douglas, 1968).
Another study included an explanation of the geometry of fabrics and the
interaction between fibers. The general relationship between stress and strain for a fabric
material is ultimately shown to be a nonlinear trend (Bulson, 1973).
1.3.3 Linear Shell Method
Another method for analyzing inflatable structures is to use a linear shell approach.
One study develops a free body diagram of a width of flexed strip of the loaded material.
Static equilibrium of forces is then applied, including the applied load and the skin
tensions on the width of the material. First, a vertical force summation is made with the
application of a small angle approximation. Then, a horizontal force summation is
developed and combined with the vertical summation canceling the skin tension terms.
The result is an expression analogous to the equation for shearing angular deflection of a
solid beam. By comparing these two equations, the internal pressure is found to be