elastic reinforced beam, bending, convergence of the small parameter method, stochastic inhomogeneity.

The bending of a pivotally fixed beam on an elastic base is considered. The initial deflection and inhomogeneity of the base stiffness are set up to small parameters. A condition is obtained that defines the boundary of the convergence region of the small parameter method. A function describing the deflection is found up to the fourth order of smallness. The case when small parameters are random variables is analyzed.

Minaeva Nadezhda Vital’evna, Doc. of Phys. and Math. Sc., Professor, Department of Mechanics and Computer Modeling, Voronezh State University, Voronezh, Russia

Sabynin Denis Victorovich, Postgraduate student, Department of Mechanics and Computer Modeling, Voronezh State University, Voronezh, Russia

Alexandr Ivanovich Shashkin, Professor, Doctor of physical and mathematical Sciences, Voronezh State University, Voronezh, Russia