The static and dynamic pre- and post-buckling characteristics of axially loaded beam structures have been widely investigated by researchers for many years. In the last few decades, there have been growing interests to expand the limits of applicability in the modeling of beam structures to the nanoscale. Different theories in nonclassical continuum mechanics have been used to do so. One of the most widely theories used in nonclassical continuum mechanics is Eringen's nonlocal elasticity theory. For certain materials, Eringen's nonlocal elasticity theory is not sufficient to model nanostructures. To overcome this obstacle, the general nonlocal theory was founded. The general nonlocal theory is a modified form of Eringen's nonlocal elasticity theory that, contrary to Eringen's, considers separate attenuation functions to account for the long-range interactions for the two different material moduli and thus introduces a second size dependent parameter. Following the introduction of the general nonlocal theory, the next steps involve integrating it into structures, such as beams and plates, to study their static and dynamic responses. As such, the considered nanobeam is modeled considering clamped-clamped boundary conditions, the Euler-Bernoulli beam theory, and the von Karman geometric nonlinearity to account for midplane stretching. The governing equations are derived by virtue of the Hamilton's principle. Interestingly, introducing the general nonlocal theory into the proposed model causes the order of the resultant transverse equation of motion to increase from fourth to sixth, thus requiring two additional higher-order boundary conditions. These additional boundary conditions are derived using a weighted residual approach and are thus variationally consistent. In this work, the effects that these higher-order boundary conditions have on the static response of the system are deeply studied. Specifically, the nonlocal parameters, Poisson ratio, and axial load are varied. The static critical buckling loads, bifurcation diagrams, and static post-buckled configurations are examined and presented. The results show the importance of selecting a higher-order boundary condition that is physically reasonable to achieve agreement with Eringen's nonlocal elasticity theory. Additionally, the results show that the selected nonlocal parameters and Poisson ratio may significantly alter the static critical buckling loads and post-buckled configurations.
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