Non-classical methods of determination critical forces of compressed rods

Abstract

Determination of the critical forces of compressed rods both in their study in universities and in the design of structures of mechanical systems is one of the difficult tasks. The analytical methods of solution used so far are of a particular nature and are based on the use of the basic homogeneous differential equation describing the buckling of a rod with a constant cross-section along the length, supplemented by simple boundary conditions at the ends, etc. It is proposed using computer technologies to significantly simplify the solution of complex problems of the stability of a compressed rod and at the same time achieve greater clarity and versatility. The application of the proposed analytical-graphic and numerical-graphic methods is shown on specific examples. The solution of test and real problems of determining the critical forces for rods of constant and variable cross-sections is shown. The proposed mathematical models and decision algorithms are verified using computational experiments. On the basis of the results obtained, practical conclusions are drawn.