Abstract
The aim of this paper is the analysis of rod cross‐ply bending and stability of rod systems in the presence of cracks. The power concept (its theoretical base is Maxwell's theorem about the reciprocity of displacements) and linear fracture mechanics methods for research of mechanical properties of rod systems in the presence of cracks nave been used. The main equation of the rod cross‐ply bending and the common solution of this equation were obtained. The expression of the relationship between rod deflection and the disturbing cross‐force was obtained. Some transcendental equation allows defining the inferior boundary of critical force of rod with a crack.
Highlights
In earlier papers, elastic beam systems with cracks in some rods were considered [6, 1, 4, 2, 5, 8]
In the present paper this concept has allowed to receive the equation and the common decision of the problem of cross-ply bending and stability of the compressed rod containing a crack in some crosssections of a rod
The relation between the rod deflection and the disturbing cross-force is obtained. It is shown there is some minimal value of the disturbing force before reaching which the crack remains closed
Summary
Elastic beam systems with cracks in some rods were considered [6, 1, 4, 2, 5, 8]. In particular an attempt to analyze of Euler’s problem for axially compressing rod with a crack in some cross-section [5, 6, 2, 7]. In all this research the concept of an elastic multicomponent hinge is used to simulate the influence of a crack on rod compliance. On the basis of this concept, there is the principle of the reciprocity works (Maxwell’s theorem). It allows defining a compliance of an equivalent elastic hinge, which influence on integral deformation of a rod coincides accurately with influence of a crack
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