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By using the Pontryagin's maximum principle, we determine optimal shape of a nonlocal elastic rod clamped at both ends. In the optimization procedure, we imposed restriction on the minimal value of the cross-sectional area. We showed that the optimization may be both unimodal and bimodal depending on the value of the restrictions and the value of characteristic length. Several concrete examples are treated in detail and the increase in buckling capacity is determined.

This paper presents an analytical investigation on the buckling and post-buckling behavior of rotating nanorods subjected to axial compression and clamped at both ends. The nonlinear governing equations are derived based on the classical Euler–Bernoulli theory and Eringen's nonlocal elasticity model. The critical load parameters such as angular velocity and compressive axial force are determined for given values of nonlocality parameter. The validity, convergence and accuracy of the solutions are established by comparing them with known classical solutions. The numerical results show that an increase in the nonlocality parameter gives rise to an increase in post-buckling deformation.

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