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In this work, we present predictive models of the buckling loads of Bernoulli-Euler nanobeams under a uniformly thermal environment based on strain-/stress-driven local/nonlocal mixture theories. The constitutive equation is expressed in local/nonlocal mixture integral form with the bi-Helmholtz kernel. The temperature effect is equivalent to a thermal load induced by the thermal expansion and boundary constraint, while the local/nonlocal mixture effects on the thermal load are taken into account. Using Laplace transform methods, the integral governing equations derived using different local/nonlocal mixture models are solved directly and exact solutions for critical buckling loads are obtained. We provide a series of numerical examples in which we present predictions of the size-effects on beams with various boundary edges. Moreover, the influence of considering the size-dependent thermal loads is also examined.

Exact solutions for buckling loads of nanobeams under thermal effect based on local/nonlocal mixture integral models with bi-Helmholtz kernel