ANALYTICAL CALCULATION OF A BEAM BASED ON AN ELASTIC WINKLER FOUNDATION WITH EXPONENTIAL INHOMOGENITY

The article is devoted to the analytical calculations for beam bending based on nonhomogeneous solid elastic Winkler base. In this paper we consider the case where the beam is subjected to a parabolic-variable transverse load and the inhomogeneity of the elastic foundation is given by an exponential function. The fundamental functions and partial solution of the corresponding differential equation of beam bending are written out in explicit closed form. These functions are dimensionless and are represented by absolutely and uniformly convergent power series. In turn, these functions are used to express the formulas for the parameters of the stress-strain state of a beam such as deflection, angle of rotation, bending moment, and shear force. The unknown integration constants in these formulas are expressed through the initial parameters, which are found after the implementation of the given boundary conditions. Thus, the calculation of a bending beam is reduced to the procedure of numerical implementation of explicit analytical formulas for the parameters of the stress-strain state. The practical application of the obtained solutions is demonstrated by an example. A prismatic concr