A geometrically and physically nonlinear model of a membrane cylindrical shell, which has been built and tested, describes the behavior of a airbag made of fabric material. Based on the geometrically accurate relations of "strain-displacement", it has been shown that the equilibrium equations of the shell, written in terms of Biot stresses, together with boundary conditions acquire a natural physical meaning and are the consequences of the principle of virtual work. The physical properties of the shell were described by Fung’s hyper-elastic biological material because its behavior is similar to that of textiles. For comparison, simpler hyper-elastic non-compressible Varga and Neo-Hookean materials, the zero-, first-, and second-order materials were also considered. The shell was loaded with internal pressure and convergence of edges. The approximate solution was constructed by an spectral method; the exponential convergence and high accuracy of the equilibrium equations inherent in this method have been demonstrated. Since the error does not exceed 1 % when keeping ten terms in the approximations of displacement functions, the solution can be considered almost accurate. Similar calculations were performed using a finite element method implemented in ANSYS WB in order to verify the results. Differences in determining the displacements have been shown to not exceed 0.2 %, stresses – 4 %. The study result has established that the use of Fung, Varga, Neo-Hookean materials, as well as a zero-order material, lead to similar values of displacements and stresses, from which displacements of shells from the materials of the first and second orders significantly differ. This finding makes it possible, instead of the Fung material whose setting requires a significant amount of experimental data, to use simpler ones – a zero-order material and the Varga material

This study investigates the combustion behavior of hydrogen–air mixtures in a closed chamber at reduced initial pressure, focusing on applications in thermal energy methods (TEMs) for plastic processing. The primary goal was to develop and validate a numerical model capable of accurately predicting pressure and temperature profiles over time. By employing ANSYS Fluent 2024 R2 and the GRI-Mech 3.0 mechanism, a detailed combustion model was constructed and validated against experimental data, adhering to the standards outlined in EN 15967: 2011. Subsequent simulations under low-pressure conditions revealed consistent flame front propagation and turbulent flow patterns, crucial factors for achieving stable temperature distributions and optimal part placement. This validated model provides a valuable tool for predicting combustion effects, enhancing safety, and optimizing the performance of hydrogen-fueled TEM processes. By leveraging hydrogen as a clean and sustainable energy source, this research contributes to a more environmentally friendly approach to plastic processing. Future studies will delve into the combustion of hydrogen–air mixtures in the presence of plastic parts to further refine the efficiency and effectiveness of TEM processes.

Completely geometrically nonlinear beam model based on the hypothesis of plane sections and expressed in terms of engineering strains and apparent stresses is applied to the structural analysis of...

The postbuckling of a Kirchhoff isotropic simply supported plate is considered in detail. The in-plane displacements on the edges of the plate are not constrained. The solution is obtained using the principle of the total potential energy stationarity. The expression for energy is written in the three versions: in terms of the Biot strains, the Cauchy-Green strains, and the strains corresponding to Füppl-von Kármán plate theory. Some approximate solution is constructed by the classical Ritz method. The basis functions are taken in the form of Legendre polynomials and their linear combinations. The obtained diagram of equilibrium states is rather similar to the classical diagrams of compressed shells. We show the failure of Föppl-von Kármán theory under large deflections. Using the Biot strains and the Cauchy-Green strains leads to the discrepancy between the results of at most 5 %. We demonstrate the high accuracy and convergence of the approximate solution.