FORMULATION AND EXPERIMENTAL-VERIFICATION OF A PNEUMATIC FINITE-ELEMENT

Many engineering structures completely surround and enclose gas filled volumes. The enclosed gas adds additional stiffness to the surroundin g structure. This paper shows how to account for this effect by means of an augmented virtual work principle. The additional term augmenting the virtual work equilibrium statement for the structure is the virtu al boundary work done by the pressure of the enclosed gas. The augment ed equations are discretized using standard finite element methods, an d the additional terms are discussed. The resulting 'pneumatic' finite element is shown to be analogous to regular structural finite element s. To assess the accuracy and efficiency and also to illustrate the ap plicability of the present formulation, a series of four examples was selected. In two of the examples, the behaviour of the end cap of a pa rtially filled plastic food product container is studied. The numerica l results using the pneumatic element compare well with an alternative Rayleigh-Ritz solution of the end cap behaviour. The other two exampl es represent the behaviour of a double bellows air spring shock absorb er under static isothermal and dynamic adiabatic conditions. For the s tatic isothermal case, an experimental study was performed with result s in good agreement with the pneumatic element solutions, For the dyna mic adiabatic loading case, the dynamic stiffness of the air spring wa s predicted using the pneumatic element. The numerical results agree w ith experimental data published in an air spring application guide. Th e examples illustrate that the pneumatic element formulation can be ap plied to the large deflection analysis of structures that enclose gas filled volumes.