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This study investigates the size-dependent buckling behavior of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment. A non-uniform temperature distribution is established through nonlocal heat conduction. Subsequently, the equivalent thermal load due to the obtained temperature distribution and boundary constraints is derived using the governing equations of the axial thermal deformation of the beams based on the stress-driven nonlocal elastic model. To obtain the critical buckling load of the nanobeams, the quadrature element method is used to numerically resolve the eigenvalue problem. In the numerical simulation section, we have presented a series of examples to analyze the effects of length-to-height ratios, nonlocal scale parameters, and Winkler-Pasternak foundation parameters on the buckling loads of the nanobeams under various boundary conditions. Moreover, we examine the effect of comprehensively considering both the elastic and thermal nonlocality on the thermal loads and finally mechanical buckling loads.

journal of thermal stresses

Investigation on buckling of Timoshenko nanobeams resting on Winkler-Pasternak foundations in a non-uniform thermal environment via stress-driven nonlocal elasticity and nonlocal heat conduction