DEFORMATION AND STABILITY OF THIN-WALLED SHALLOW CONICAL SHELLS UNDER EXTERNAL PRESSURE AND PERIODICALLY DISCRETE BORDER FIXATION - Bessmertnyi, Y. O. (Computer Science and Applied Mathematics, 2017)
A numerical study (within ANSYS software) deals with deformation and buckling of series of elastic isotropic flat closed conical shells subject to external normal uniform pressure. Fixation of shells edges is periodically discrete (movable-support sections alternate with hinged-support sections of the same length). Length of each periodic fixation is the same, and the total length of mobile fixation is equal to the total length of immobile fixation. While loading, the type of shells fixation causes periodically nonuniform stress-strain state in the circumferential direction. Periodicity of subcritical stress-strain state is equal to a number of fixed sections that varies in a wide range from zero up to fourteen and infinite. In this case zero corresponds to continuous mobile fixation, infinite – continuous immobile fixation, from two up to fourteen corresponds to periodic boundary conditions. The phenomenon of “static resonance” was found for conical shells. The essence of the effect is as follows. Minimum limit pressure of geometrically nonlinear analysis corresponds to the periodicity of stress-strain state of a conical shell which coincides with a half-sum of the periodicity of the first eigenvibration mode of an unloaded shell and the first eigenmode of linear buckling problem of a continuously hinged supported shell subject to external pressure. All results are presented in form of graphs and tables for each type of calculations – linear problem of stability (bifurcation) and geometrically non-linear problem of stability. The results of this work make possible to forecast the “static resonance” phenomena for shell with heterogeneous stress-strain state on the basis of two simple linear calculations.