Buckling of compressed rods taking into account their own weight under different boundary conditions

Abstract

Abstract The article is devoted to the problem of calculating the stability of compressed rods taking into account their own weight. The fourth order resolving differential equation with respect to dimensionless deflection was obtained. A technique for the numerical solution of the resulting equation is proposed using finite differences method. As a result, the problem was reduced to a generalized eigenvalue problem. Comparison with the solution of other authors is given.