Application of the Projection-Iterative Scheme of the Method of Local Variations to Solving Stability Problems for Thin-Walled Shell Structures Under Localized Actions

The tasks of the stability of reinforced spherical shells that are part of the extended inhomogeneous structures are investigated under localized actions based on the developed new projection-iterative version of the method of local variations. Stability under local loading implies the performance of thin-walled shell structures in rocket and space equipment, antenna and waveguide technology, as well as power engineering. Under localized actions, there is a significant concentration of stresses and strains. The methods for solving relevant tasks are rather complex, multiple-mesh variational-difference schemes are within the area of focus. For the tasks of stress-strain state and stability under considerably inhomogeneous stress states, the local variation method is effective, but it requires more computation time as compared with the Ritz-type finite difference and variation methods. Noteworthy is that this leads to the need to develop more adequate schemes for its implementation based on the concept of projection-iterative methods. This scheme of the method of local variations is analyzed, its convergence is investigated, and the practical efficiency associated with a significant decrease in computation time for numerical implementation is shown. The tasks of the stability of complex shell structures with spherical shells reinforced by support rings under the exposure of local loads are considered. The experimental investigation data are given. The calculated data of the critical forces and the configuration of the waveforms are corroborated experimentally.