Miednikova M. The influence of circular holes on the stress-strain state of cylindrical shells of finite lengths during torsion

The dissertation work is devoted to the study of the stress-strain state (SSS) of elastic isotropic cylindrical thin-walled shells of finite lengths, weakened by a circular hole under the action of a torque. With the help of linear and geometrically nonlinear analyses with finite element method (FEM), the influence of changes of geometric parameters on the stress state, in particular on stress concentration factor, has been investigated. Effective grid models have been developed for solving the problems of determining stress-strain state in cylindrical shells with a hole, on the basis of liner FEM-analysis, based on the use of adaptive grids together with specially formulated methods of accuracy control It is shown that mathematical model of A. Lurie is applicable for large length shells and for small size of a hole, and is unsuitable for short shells and for shells weakened by a large hole. This model can overestimate the results of solving the problem of determining the level of stress concentration many times over in relation to the deformation of shells of finite lengths. For a wide range of changes in geometric parameters of shells, the results obtained in the nonlinear formulation are close to results from the linear solution only for the initial stage of loading and in a rather narrow range of loads. Taking into account the geometric nonlinearity of deformation, stress fields and displacement fields with increasing load, especially when approaching the depletion of the bearing capacity, undergo qualitative changes, both at the boundary and in a significant area around the hole. The main attention is paid to the study of the stress concentration and dependences of stress concentration factor on the load value, shell length and hole size. Stress concentration factor increases with increasing load for al and studied casings. The exception is shells of large length with a small hole size, for which it is practically independent from the load level. It is obtained that there is a certain length determined by calculations, with a decrease of this length the supporting effect of the shell edge begins to bear on, which significantly decrease level of stress concentration. The results of the research were used in practice of the State “Design Office “Yuzhnoye” named after M. K. Yangel” in the design of a space rocket, in particular adapter and head fairing as part of an international contract. Key words: finite element method, cylindrical shell, circular hole, torsion, stress-strain state, stress concentration factor.