Abstract
The paper deals with the problem of calculating the rod structure of a two-tier dome for stability. Such structures consisting of straight rod elements are widely used in practice and have a number of significant advantages. First of all, it is a high rigidity with a low mass. Also, this type of construction is well resistant to dynamic loads. At the same time, the dome model allows for the bifurcation of points on the equilibrium state curve of the system. The problem of the dynamic stability of double dome is solved by the principle of stationarity of total potential energy of the system. The analysis of the obtained solution is carried out, and the equilibrium state diagram for a two-tier core dome is constructed.
Highlights
Spatial rod structures in the form of shells of rotation consist of straight prismatic elements connected at nodes and belonging to a curved surface
A significant role is played by the characteristic of the degree of flatness of the considered rod structure of the two-tier dome, which is estimated by the ratio of the diameter of the horizontal circle of its base to the height
It is known that for d/h ≤ 8 the dome model allows for the case of bifurcation of points on the equilibrium state curve of the system [1, 2]
Summary
Spatial rod structures in the form of shells of rotation consist of straight prismatic elements connected at nodes and belonging to a curved surface. The results of a numerical and experimental investigation into static stability of externally pressurized hemispherical and tori spherical domes are considered in [3, 4]. It revealed many difficulties which exist when dealing with layered metallic shells [5]. The development of new approaches for engineering calculations of dome structures is relevant, but before proceeding to the study of the stability of rod structures in the form of convex polyhedra, let us find out the conditions that can correspond to the beginning of the branching points of the deformation curves for specific models of spatial configurations.
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