Size‐dependent buckling loads of non‐uniform Bernoulli–Euler beams with elastic boundary conditions and thermal effects based on two‐phase local/nonlocal elastic model

Abstract We present predictive models of the size‐dependent buckling loads of non‐uniform Bernoulli–Euler beams under thermal effects based on the two‐phase local/nonlocal elastic model. The beam ends are assumed to be constrained by elastic springs with translational and rotational stiffness to simulate general boundary conditions. In contrast to most literature in this field, both the bending and thermal deformations of the beams are simultaneously considered to be two‐phase local/nonlocal of two phases, that is, the thermal effect is taken as equivalent to a size‐dependent thermal load. By using the fully equivalent differential form of the local/nonlocal equation with a set of constitutive boundary conditions, the problem is solved numerically with the aid of the generalized differential quadrature method (GDQM). Through conducting validation study, several parametric studies are given for examining the effects of the slope of beams’ thickness variation, nonlocal parameter, and elastically supported conditions on the buckling loads of non‐uniform beams. The results show that constrained stiffness has a drastic influence on the critical bucking loads of the beams. Furthermore, the consideration of the two‐phase thermal load will further reduce the actual buckling load of the beams.