Numerical study of the effect of individual racks in lenses on the operation of nonlinear lenticular membrane-pneumatic systems by the step method

Abstract

Objective. The purpose of this study is to substantiate the methodology for static calculation of light coatings for large-span structures with lenticular membrane-pneumatic lenses, including racks at individual points of the span, using the step-iterative method of parameter increments.Method. The study involves the phased application of the finite element method (FEM), the universal equation of state of gas and the improved Euler-Cauchy numerical procedure, taking into account the geometric nonlinearity of systems and the physical nonlinearity of the elastic work of air in lenses and taking into account the aftereffect of excess air pressure.Result. A comparison is made in terms of rigidity and load-bearing capacity of membrane-pneumatic lenses, reinforced with individual posts, with the corresponding flexible membrane-pneumatic lenses of the classical type.Conclusion. In the presence of racks, the effect of a significant increase in the rigidity and bearing capacity of lenticular membrane-pneumatic systems is observed for large spans. The distance between the posts along the building can be adjusted during the design and thereby regulate the effect of strengthening the system. The maximum deflections of the lenticular-shaped membrane-pneumatic system reinforced with struts are much less than the maximum deflections of the lenticular membrane-pneumatic system of the classical type under the action of the calculated snow load of the first and second limit states.

Keywords

• step - an iterative method of parameter increments
• an improved numerical eulercauchy procedure
• taking into account the geometric and physical nonlinearity of the elastic properties of air in the pneumatic cavity
• membrane-pneumatic lenses of the classical type