Relevance. The use of shells as thin-walled structures for various industries is very diverse. Spherical shells are widely used in the aircraft industry, circular cylindrical shells are used in the oil and gas industry, and more than 30 analytical forms of shells have been used in the construction industry. All elements of shell structures are undoubtedly subject to various strength calculations. Also, a separate role in the study is occupied by the experimental part, which confirms or refutes the calculated equations, this indicates the undoubted perspective and relevance of modeling the loading of shell structures. The aim of the study is to assess the condition of a thin-walled shell under three-parameter loading by tensile, compression and torsion forces. Methods. Experimental studies on the deformation of shells carried out in laboratory conditions on prototypes made of steel 45 GOST 1050-2013 are presented, and the loading conditions of the sample are modeled, similar to the possible conditions for applying loads to existing structures. Results. Experimental diagrams of deformation of the sample material in various planes are given, the development of deformation of the shell after applying joint efforts of stretching and torsion, as well as compression and torsion to the destruction of the material is estimated. For the relevance of the conducted experiment, a real design has been selected, which, when certain conditions are created, can experience appropriate experimental loads.

Reviewing the numerical simulation of the process of non-proportional elastic-plastic deformation of steel 45 by a knot of constant curvature, taking into account the complex nature of deformation under complex subcritical loading by axial compressive force and torque for a thin-walled circular cylindrical shell. The theory of Quas and simple processes of A. A. Ilyushin and the mathematical model of V. Zubchaninov were applied taking into consider the parameters of the complex loading for plane trajectories To assess the accuracy of accepted theories, the simulation results are compared with experimental results, received on the automated complex СNcomputer in the laboratory of the faculty of «Strength of materials and theory of elasticity and plasticity» of the Tver state technical University. Was introduced the scheme of calculations disproportionate plastic deformation of steel 45 using the proposed mathematical model showed a satisfactory result and recommended for further use. Remarks, that in the described processes the lack of some parameters complex loading in approximations reduces the accuracy of the final calculated values, differences significantly compared to the experimental data.

The article summarizes results of experimental studies of stability in circular cylindrical shells under combined loading by compressive force, internal pressure and torsion at the SN-EVM unit, developed by the Department for Strength of Materials, Theory of Elasticity and Plasticity at Tver State Technical University. It gives description of the test facility and methodology of experiments for studying the elastoplastic properties of materials under combined loading. It cites the processed experimental results for comparison with the formulated theory of bifurcation for the thin-walled circular cylindrical shell.

Thin-walled cylindrical shells are used in elements of highly loaded products of mechanical engineering and energy. Along with their frequent use in production, experimental research in laboratories is also carried out constantly. This allows to simulate the behavior of the shell when exposed to external forces. But sometimes conducting an experiment becomes little possible due to the limitation of the power of the experimental apparatus when modeling the corresponding conditions of exposure to the shell in practice, therefore, improving theoretical methods for calculating the limiting states of shells when working in the elastoplastic region is relevant. The purpose of the study is to verify the conformity of the results of the experiment conducted on a thin-walled cylindrical shell made of steel 45 (GOST 1050-2013) when exposed to the sample by stretching, compression and torsion forces with theoretical calculations based on the equations of the theory of elastic-plastic processes by A.A. Ilyushin. The equations of the defining relations of the theory of elastic-plastic processes by A.A. Ilyushin for arbitrary trajectories of complex loading and deformation of materials in the deviatory deformation space Э1-Э3 are presented. All theoretical results are checked for compliance with the experiment, the reliability of the existing theory of stability is assessed. The solution is presented in the form of graphs of the dependence of the vector and scalar properties of the material on the length of the arc of the deformation trajectory and other parameters. Numerical values are selectively presented for different loading stages.

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