A simple finite element framework for modelling pneumatic structures

Abstract

Besides material and geometric stiffness, usual components affecting tension structures in general, pneumatic structures are endowed with a pneumatic stiffness, which corresponds to a reluctance of the pressure envelope to change its volume. The higher the inside pressure, the more relevant this component can be. Researches on the nonlinear behavior of pneumatic structures usually consider finite strains, which might indeed be necessary to analyze highly pressurized system. Most civil and architectural applications, however, are subject to low to moderate pressures, with materials undergoing small strains, for which simplified material models may suffice, provided that a sound model to cope with membrane wrinkling is also considered.This paper presents a simple yet effective model to cope with the nonlinear analysis of pneumatic membranes under wind loads, incorporating an effective wrinkling criterion into Argyris’ membrane element, and deriving new expressions for its pneumatic stiffness. The model was tested through an inexpensive experiment, comprising the compression of an exercise ball, which corroborated the importance of considering variable inside pressures, for moderate-pressure systems. This relevance reduces, however, as the dimensions of the structures increase, especially in the case of large insufflated domes.