Longitudinal Compression of a Rod with Initial Deflection Acquiring Induced Anisotropy

The paper considers a compressed-bent flexible rectilinear rod having an initial imperfection in the form of deflection. The heterogeneity of the stress state from bending leads to a tightening of the deformations that cause the elastic characteristics of the material to vary. The theory of deformation of bodies in inhomogeneous stress fields with induced anisotropy of properties proposed earlier by the authors is used to obtain the equation of the rod in the deflected state. The heterogeneity of the stress field causes the elastic characteristics of the material to vary, resulting in changes in the design parameters of the structure. The solution is based on the numerical realization of the curved axis equation using the method of variable elasticity parameter. A marked increase in the compressive force corresponding to a significant increase in deflections compared to the bifurcation approach is found.