Exact solutions for post-buckling deformations of nanorods

Post-buckling configurations of nanorods with various end conditions are described by means of exact analytical solutions of the nonlinear differential equations governing equilibrium configurations of rods that are made of an Eringen’s nonlocal material and deform according to the kinematics of Kirchhoff’s theory. The general solutions in terms of Weierstrass elliptic functions of the equilibrium equations for planar flexural deformations of naturally straight rods are deduced; then, these solutions are specialized to rods subject to compressive axial forces and applied to the study of post-buckling behavior. Comparison of the results for nonlocal and classical rods having the same geometry and tensile modulus shows that the former exhibit, with respect to the latter, a reduction in rigidity that becomes more significant for greater values of the material parameter which accounts for small-scale effects in the response of an Eringen’s nonlocal material.