Stability of bars with variable rigidity

A heterogeneous in length bar with a variable cross-section is considered. The axis of a bar, which joins the centers of gravity of all the cross-sections, is a straight line. The bar is compressed by a longitudinal force applied to the center of gravity of the boundary cross-section. The article describes the case of stability loss of the straight-line form of equilibrium of a bar, when both, linear and curved forms are possible. Approximate analytical formulas for critical compressive force in four cases of boundary conditions for periodically heterogeneous bar are obtained. In case of a bar with a stepped variation of its cross-section and which consists of only one period (the limiting case) the comparison of results, computed using obtained formulas, with exact solutions of stability equation known before is made.