Method for static calculation of non-linear membrane-pneumatic systems

Abstract

Objective. The aim of the study is to develop a methodology for the static nonlinear calculation of membrane-pneumatic systems for force loads and various impacts.

Method. The calculation of nonlinear lens-shaped membrane-pneumatic systems is based on the wellknown stepwise method of parameter increment and the possibilities of the iterative process of the Euler-Cauchy numerical procedure with an increased number of iterations, using the finite element method at each step. Since the calculation of pneumatic systems based on compressed air is performed, a system of equations is used that includes a universal equation of state of a gas and a formula for determining the pressure increment in a sealed space formed by the lens-shaped roof of the structure.

Result. A modified iterative method of parameter increment and a corresponding numerical approach are presented, which improve the accuracy of solving nonlinear equations. The main improvement lies in increasing the number of iterations from the usual three to thirty. A lens-shaped membrane-pneumatic system with a span of one hundred twenty meters was calculated for the action of a sectional snow load distributed over a half-span.

Conclusion. The proposed method can be used to calculate not only lens-shaped structures, but also air-supported and pneumatic-framed objects.