Investigation of the Stress-Strain State of the Plate in the Place of Its Fixing on the Basis

Abstract

In mechanical systems and building structures, the joint of parts as a sheet or a thick plate rigidly fixed on the basis are rather common. Compliance of contacting elements of the structure leads to non-uniform distribution of the unit load in their contact zone, thus essentially affecting the strength and rigidity parameters of individual parts and structures as a whole. In this connection, the problem of determining the law of variation of the unit load and stresses in the place of the plate fixing on the basis becomes relevant.This paper considers the method for determining the pointed power factors, implying the representation of the plate as the beam on the elastic basis, for which the Timoshenko equation is valid, that is, the equation of relation of power factors and bending and shearing strains. The differential equation of the stress-strain state is solved analytically by the Euler method, accounting for the fact that the beam is subjected to constraint bending and the law of variation of the unit load is of aperiodic attenuating oscillations.The obtained analytical relations and plotted on their basis diagrams indicate that the unit load is highly concentrated at the boundary of the plate and the rigid basis, the value of this load exceeding its average value dozens of times. Investigation results allow for performing the strength and rigidity calculation of the sheet or the thick plate fixed on the basis with a high degree of accuracy, which is urgent when designing the units of mechanisms and building structures.