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OStability of Bars with Variable Rigidity / Gorbachev V.I., Moskalenko O.B. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 6. P. 65-69 [Moscow Univ. Mech. Bulletin. Vol. 65, No 6, 2010. P. 147-150]. A variable cross-section bar is considered. The bar is not uniform in length. The bar axis through the mass centers of all cross sections is a straight line. The bar is compressed by a longitudinal force applied to the mass center of the boundary cross section. The stability loss of the straight-line shape of the bar's equilibrium is discussed when a curved shape is also possible. Approximate analytical formulas are obtained for the critical compressive force when four types of end fixing are used for a periodically nonuniform bar. The numerical results obtained by these formulas are compared with the known exact solutions to the stability equation for a bar whose cross section is stepwise variable and whose nonuniformity consists of only one period (the limiting case).
Key words: elasticity, stability, heterogeneous bar, averaging method.
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