ABSTRACT
This chapter provides substantiation of the I. G. Bubnov-B. G. Galerkin method for structures constituting a statically determinate column of a variable section with a single rigid support or two hinged supports at the ends. There is a simple method for stability analysis of systems with an infinite number of degree of freedoms, which was developed during the period of 1913–1915 by Russian scientists: naval engineer professor Bubnov and professor of mathematics Galerkin. The Bubnov-Galerkin method is used for stability analysis of systems, the equilibrium states of which are specified by linear differential equations and linear boundary conditions. The Bubnov-Galerkin method prescribes investigation of the stability of a system’s equilibrium states by means of equations. A possible application area for this method is stability analysis of rectilinear structures consisting of sequentially connected prismatic members positioned in a straight line. In the Bubnov-Galerkin method, there is the possibility to estimate the error of the obtained critical structure buckling load.
