Stress-deformed state of the shell with a small initial deflection under the action of the end load

Abstract

Purpose of work. Construction of method for calculating the stress-strain state of cylindrical shell with small initial deflection, to which an end load is applied, using the method of characteristics. Comparison of the calculation results of the obtained model with the works of other authors in this area.
 Research methods. For the calculation, the equations of motion of the Timoshenko type shell were used, taking into account both the shear deformation and inertia of rotation, and some nonlinear terms, to which the method of characteristics was applied. To obtain the equations of shell motion, the Hamilton-Ostrogradsky variational principle was used.
 Results method is proposed for calculating the stress-strain state of a cylindrical shell with a small initial deflection using characteristics. Comparative analysis of the calculation results with research in this area by other authors, which showed the effectiveness of the proposed method.
 Scientific novelty. The equations of the classical theory of shells, based on the Kirchhoff-Love hypotheses, which do not take into account the shear deformation and inertia of rotation, as well as linear equations of the Timoshenko type, have become widespread. In this work, a model of the stress-strain state of an axisymmetric shell with small initial deflections is constructed, taking into account both shear deformation and rotational inertia, and some nonlinear terms.
 Practical value. The proposed method can be used to calculate the stress-strain state of structures in which thin shells are present as elements, taking into account small initial deflection. This method makes it possible to study the influence of the characteristics of the initial deflection on the stress-strain state of the entire structure.