ПРОДОЛЬНОЕ СЖАТИЕ СТЕРЖНЯ С НАЧАЛЬНОЙ ПОГИБЬЮ, ПРИОБРЕТАЮЩЕГО НАВЕДЕННУЮ АНИЗОТРОПИЮ

Abstract

A centrally compressed flexible rectilinear steel rod is considered. Due to the existing initial imperfection in the form of a perish, the rod works as a compressed-curved one. The inhomogeneity of the stress state from bending leads to the constraint of deformations that cause a change in the elastic characteristics of the material. To obtain the equation of the rod in the deflected state, the incremental theory of nonlinear deformation of bodies in inhomogeneous stress fields with induced anisotropy of properties proposed earlier by the authors is used. The inhomogeneity of the stress field causes the variability of the elastic characteristics of the material, which, due to the induced incremental curvilinear anisotropy, lead to a change in the design parameters of the structure. The solution is based on the numerical implementation of the curved axis equation using the method of variable elasticity parameter. The growth of deflections at the stages of sequential loading with increasing force is analyzed. Various variants of initial curvatures, including vanishing small ones, are considered. Regardless of the magnitude of the initial deflection, a noticeable increase in the compressive force was found, corresponding to a significant increase in deflections compared to the bifurcation approach.