Algorithm for numerical calculation of nonlinear lenticular membrane-pneumatic systems by iterative method of parameter increments taking into account the aftereffect of air pressure

Abstract

Objective. The purpose of this study is to create a static calculation algorithm to determine the maximum bearing capacity of a lenticular membrane-pneumatic system for covering large spans under the action of external force loads.Method. A numerical study of a large-span membranepneumatic structure was carried out by the step method of incrementing parameters using the finite element method and the Euler-Cauchy numerical procedure of the third order of accuracy at the step.Result. The authors have developed a technique for computer static calculation of geometrically and physically nonlinear lenticular membrane-pneumatic systems of coatings for large span structures by the iterative method of parameter increments with the phased application of the finite element method in the form of the displacement method, the universal equation of gas state and the improved Euler-Cauchy numerical procedure of the third order of accuracy.Conclusion. Ignoring the aftereffect in the calculations means the imbalance of the system due to unbalanced pneumatic forces calculated with an error of 11.2% and affecting, as the calculations showed, in the amount of approximately 7% percent on the increment of excess air pressure in the lens.