Inflated cylindrical envelope subjected to axial compressive load

TR Number



Journal Title

Journal ISSN

Volume Title


Virginia Polytechnic Institute


Inflated fabric is being considered as new structural material at the present time. It can be used in certain applications with the advantage of reducing the weight of structures, it is adaptable as an architectural element of construction; moreover, it may be developed to be one of the most economical, and simple structural materials in the future.

A number of experimental investigations of these inflated fabric structures has been studied by research units of airship and fabric companies. However, due to the difficulties of solving such problems by analysis, there is still lack of theoretical methods, even approximate solutions.

The purpose of this thesis is to investigate theoretical analysis for finding the relation between the applied load and the deflections, stresses, and also the end shortening of an inflated cylindrical fabric envelope subjected to axial compression, by the energy method. A cylindrical shape is selected because sphere and cylinder are considered more general in use and more easily to be treated than any other geometrical shapes. Also, for the sake of simplicity, a constant internal pressure is assumed in the analysis.

The use or large deflection theory for finding the critical buckling loading of thin shells was first advanced by Von Karman and Tsien (reference 6 and 7). Based on their conception; numerous studies concerning the buckling strength under various loadings have been investigated by others subsequently. The strain-displacement relation in their papers is expressed in the following form including terms up to second order:

εx= ∂u/∂x+(½)(∂w/∂x)² εx= ∂v/∂y+(½)(∂w/∂y)²-(w/R)

In this thesis, although the idea is applied to develop an analysis by the energy method, the strain-displacement relation is expressed in a different way which will be shown in the following sections.

Generally, in avoiding the mathematical difficulty of solving the differential equations obtained from the energy expression, most boundary-value problems in the theory of elasticity may be solved by assuming a solution in the form of a series which satisfies the boundary conditions, then minimizing the energy expression to determine the values of unknown parameters in the assumed solution. In this thesis, instead of using the variational method mentioned above, a graphical method for solving the differential equations is presented. However, owing to the fact that not all of the boundary conditions are specified at one point, the final results have to be obtained. by trial and error.