Calculation of the lens-shaped coating of a membrane-pneumatic structure taking into account nonlinear factors

Objective. The aim of the study is to develop and test a calculation method for lens-shaped membrane-pneumatic roofs taking into account geometric and physical nonlinearity. The relevance of the problem is due to the interest in pneumatic structures in construction practice, where a reliable and cost-effective solution for covering large spans is required.

Method. The study applies an improved iterative method of parameter increments based on the Euler and Euler-Cauchy numerical procedures. Unlike classical approaches (FEM, Newton-Raphson algorithms, the method of successive loadings), the proposed method is more resistant to error accumulation and provides the ability to adjust accuracy by changing the number of iterations and the loading step. For practical implementation, a software package has been developed that allows for taking into account both geometric and physical nonlinearity, as well as the internal pressure in the shell.

Result. Numerical modeling showed that for a 60-meter span, geometric nonlinearity is approximately 7%, while physical nonlinearity is approximately 6%. Calculations for various spans (60–100 m) confirmed the pattern of increasing nonlinearity with increasing roof size. The results demonstrate that the use of linear methods leads to an underestimation of deformations and an underestimation of the structure's load-bearing capacity.

Conclusion. The use of a modified parameter increment method improves the accuracy and reliability of calculations for lenticular pneumatic structures while maintaining acceptable computational complexity. The developed methodology and software package can be recommended for engineering calculations, the design of sports and exhibition facilities, and temporary pavilions. The practical significance of this work lies in the optimization of material consumption and increased operational reliability of pneumatic systems.

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