Nonlocal thermal-elasticity for nanobeam deformation: Exact solutions with stiffness enhancement effects

Abstract

The nanomechanical response for a nanobeam under thermal effects is investigated by using the nonlocal elasticity field theory, which was first proposed by Eringen in the early 1970s. The nonlocal constitutive relation is adopted to determine the strain energy density which considers the history of nonlinear straining with respect to an unstrained state. Based on the variational principle and integrating the straining energy density over the entire domain of interest influenced by a temperature field, a new higher-order differential equation and the corresponding higher-order boundary conditions are derived. The thermal-elastic effects of typical nanobeams are presented where new exact analytical solutions with physical boundary conditions are derived. Subsequently, the effects of the nonlocal nanoscale and temperature on the nanobeam transverse deflection are analyzed and discussed. It is observed that these factors have a significant influence on the transverse deflection. In particular, the nanobeam stiffness is greatly enhanced, or the transverse deflection is significantly reduced, with an increasing nonlocal stress effect. A conclusion is drawn that at low and room temperature the nanobeam transverse deflection decreases with an increasing temperature difference, while at high temperature the transverse deflection increases as the temperature difference increases.