THE DYNAMIC STABILITY OF PRISMATIC SHELLS
Research into the stability of prismatic shells exposed to dynamic loads is one of important problems of structural mechanics. Such shells are widely used in various fields: construction, mechanical engineering, machine building. The research presents the methodology of dynamic stability analysis of plate systems such as prismatic shells, taking into account physical nonlinearity of the material. The authors investigate the prismatic shell subject to dynamic compression load in the longitudinal direction x . The calculations are based on the Kirchhoff-Love hypotheses, particularly the hypothesis of a nonlinear elastic body. The shell material is deemed as physically nonlinear, the strain diagram is approximated in the form of a cubic polynomial. The displacements of points are determined in the form of expansions by Vlasov. In order to derive nonlinear differential equations, the energy method and the variational Vlasov method have been used. The extreme value of the total energy is determined using the Lagrange equations. As a result, we obtained the system of differential equations for studying the dynamic stability of prismatic shells taking into account the physical nonlinearity of the material. In accordance with the designed method the authors have calculated the stability of a closed shell (i.e., a prismatic shell with the closed contour of the cross section) under central compression under the action of a dynamic load (for the given geometric parameters of the shell). The edges of the shell rest on the diaphragm. The buckling of the closed shell occurs in the longitudinal direction x along one half-wave of a sinusoid. When addressing the problem, a system of nonlinear differential equations is derived, the numerical integration of which is performed by the Runge-Kutta method. Based on the calculation results, we have plotted the graphs of the relative displacement ζ of the nodal point of the shell cross section on the dynamic coefficient Kд (with and without taking into account the physical nonlinearity of the material). We have also investigated the influence of the degree of physical nonlinearity of the material, the rate of change of compression load, and the initial imperfection of the shell on the criteria of the dynamic stability of the prismatic shell.