analogous to an effective shear modulus. This is used to determine the effect of pressure
on the shearing deflection (Topping, 1964).
Another source applies continuum mechanics to membranes to obtain several
general relations. It defines the kinematics, deformation, strain, strain rate, and stress for
membranes. Balance laws are used to derive general mass balance, momentum balance,
and energy balance relations (Jenkins, 2000, pp. 49-64). To model wrinkling in beams, a
tension field model is developed with an approach for application to linear finite element
method (Jenkins, 2000, pp 103-105).
1.3.4 Finite Element Analysis Approach
Another approach is to apply finite element analysis to inflated structures. Finite
element analysis can yield accurate results for problems with complex analytical
solutions. One study compares results from the modified traditional beam theory with
finite element results. An assumption of Brazier's effect is used here. This states that as
the tube deforms due to bending and the cross-section becomes flatter, the bending
stiffness of the entire beam decreases. This is most likely due to geometry changes that
affect the area moment of inertia.
This study formulates finite elements of geometrically nonlinear motion of
membrane. These allow for changes in length of the elements to account for stretching of
the material in the ends but not in the cylinder. Triangle elements are used to model the
circular end caps and quad elements are used to model the cylindrical tubing. A pressure
relationship is used to apply a force to each element. FEA results match theoretical
results from the modified traditional beam approach.
An analysis of tubes containing multiple pockets is conducted as well. The
behavior of these multi-cellular inflated beams is shown graphically. By increasing the