Construction of a Solution of the Problem of Stability of a Bar with Arbitrary Continuous Parameters

Abstract

We consider the problem of stability of a bar with arbitrary continuous variable flexural stiffness compressed by an arbitrary continuously applied variable axial longitudinal force. For the first time, we construct the exact solution of the corresponding differential equation of longitudinal bending. As a result, we obtain the formulas for displacements and internal forces in any cross section of the bar in the analytic form.