Application of the G.A. Geniev, N.S. Chausova method for stability of shallow shells investigation

Abstract

Introduction. The work is devoted to the stability of shallow shells investigation, based on the G.A. Geniev, N.S. Chausov methodology. An analysis is given of the works of the authors working on the issues of determining the stress-strain state of this structure type. Current trends and shortcomings of the methods used are indicated. Materials and methods. The analysis of stability is based on the G.A. Geniev, N.S. Chausov fundamental work. It defines the first and second kind stability lost and substantiates the use of an equations system to describe the stress-strain state of a structure. The equations system for shallow shells with constant and variable thickness and shape of the middle surface is solved using the Bubnov – Galerkin method. The approximating functions of stresses and displacements make it possible to vary the type of structure support. Results. Implementation of the G.A. Geniev and N.S. Chausov methodology with V.Z. Vlasov approximating functions made it possible to investigation the influence of various parameters on the critical load. The geometric nonlinearity of the work of structures was taken into account. Specific values of the design parameters are given, which increase the second kind stability with constant initial data. Conclusions. The analysis of the shallow shells stability made it possible to reveal the regularities in the change in the value of the critical load when varying various geometric characteristics. The presented results can be used in the design of real structures. At the same time, it is possible to set the tasks of optimizing such structures with restrictions on the value of their volume (weight) or minimizing it due to the interconnected change in geometric characteristics while maintaining the bearing capacity.