Influence of the Type of Basis Functions in the Bubnov-Galerkin Method in the Deformation Analysis of a Compressed-Curved Rod with Induced Anisotropy

The paper considers the longitudinal bending of a flexible rectilinear rod. The heterogeneity of the stress state in the deflected state leads to constrained bending deformations, which cause changes in the elastic characteristics of the material. The equation of the bent axis of the rod in the deflected state uses the theory of deformation of bodies in inhomogeneous stress fields with induced anisotropy of properties proposed earlier by the authors. The solution was obtained by the Bubnov-Galerkin method based on the analysis of rod deflections using various basis functions. Regardless of the choice of the approximating function, a marked increase in the compressive force corresponding to a significant increase in deflections is found compared to the bifurcation approach.