On the Applicability of the Relations of the Cubic Timoshenko-Type Theory of Shells to the Study of the Postcritical Behavior of Rods

The question of whether the nonlinear Timoshenko-type theory of shells can be applied to the study of the initial postcritical behavior of a rod under compression is considered. The Koiter asymptotic theory in the Budyanskii form is used. The exact solution of the problem is obtained and a formula for the coefficient of postcritical behavior allowing for the effect of lateral-shear strains is derived. It is shown that the expressions (specified to within cubic terms) for lateral-shear strains and curvature permit us to use the nonlinear theory of shells to analyze the initial supercritical behavior of rods