Generalization of Saint-Venant principle to kinematic boundary conditions for beams.

The modern formulation of the Saint-Venant principle allows us to assert that the disturbance of the stress-strain state caused by statically equivalent loads attenuates quickly enough at some distance from the places of application of loads, which can be called the effect of static heterogeneity. This principle is widely used in the calculation and design of building structures, for example, rods operating under tension, compression and bending, since it allows, neglecting complex functions of stresses and deformations near the places of application of loads, to obtain more easily realizable results in practical terms. The article provides a historical overview of the Saint-Venant principle, its subsequent development, application, as well as its modern interpretation. Numerical experiments carried out within the framework of this paper made it possible to reveal the similarity in the behavior of the stress and strains functions under conditions of static inhomogeneity with other types of inhomogeneities, which we will divide into four groups: geometric, physical and mechanical, static and kinematic. Within the framework of this work, the application of the Saint-Venant principle to the kinematic inhomogeneities of the boundary conditions was generalized. Using numerical modeling techniques in the ANSYS Mechanical APDL software package, two options for the implementation of rigid anchoring, representing inhomogeneous kinematic boundary conditions, were considered. The reliability and correctness of the results of numerical experiments is justified by the mesh convergence carried out, as well as by comparison with solutions by strength of materials. As well as for static inhomogeneity, the stress distribution in the places of inhomogeneous kinematic boundary conditions can be represented as the sum of solutions by the methods of strength of materials and some self-balanced function, which rapidly decays with distance from the disturbance zone. The considered self-balanced function forms the stress-strain state near various kinds of inhomogeneities. [ABSTRACT FROM AUTHOR]