Features of Accounting for Geometric and Physical Nonlinearities in Long-Span Pneumatic Membrane Systems

Abstract

Objective. The purpose of the study is to substantiate the need to take into account the geometric and physical nonlinearities in large-span membrane-pneumatic systems.Method. The study is based on the application of the parameter variation method; method of successive loadings; the iterative method of parameter increments using the third Euler-Cauchy numerical procedure or the Runge-Kutta method of a higher order of accuracy.Result. It has been established that the geometric non-linearity can be from 5 to 10% if the structure has a small or medium span, and the load on the structure is not very large, especially when it comes to section load. If the span of the structure is 120150 meters, and the load and deflections are large enough, then the geometric nonlinearity can be 20% or more. It was revealed that the physical nonlinearity, which we took into account by the standard Euler-Cauchy procedure of the third order of accuracy, with a large span of the structure and a large load is approximately 13-21%, and the part of the physical nonlinearity of the air pumped between the hermetic membranes of the structure is determined using an improved formula Euler-Cauchy with the number of iterations 20-25, i.e. "aftereffect", according to the results of the study, ranges from 2-7%.Conclusion. A structure consisting of light metal structures can be erected within a few months on a finished pile or strip foundation. Such structures can easily withstand many types of dynamic loads, namely wind, seismic, vibration, and are one-third cheaper than buildings made from traditional materials.

Keywords

• non-linear building mechanics
• step-by-step methods for solving problems
• calculation of a structure taking into account geometric and physical nonlinearity
• iterative euler-cauchy method of the third order of accuracy