Nonlinear Thermal Bending for Shear Deformable Nanobeams Based on Nonlocal Elasticity Theory

Nonlinear bending of shear deformable nanobeams subject to a temperature field is investigated in this paper based on von Kármán type nonlinearity and nonlocal elasticity theory. By using the variational principle approach, new higher-order governing differential equations and the corresponding higher-order boundary conditions both in the transverse and axial directions are derived and discussed. Several examples are presented to highlight the effects of nonlocal nanoscale, temperature and shear deformation on the transverse deflection of nanobeam. The exact analytical solutions for transverse deflection are derived and the solutions confirm that the nonlocal nanoscale tends to significantly decrease nanobeam transverse deflection while shear deformation increases the transverse deflection of nanobeam. It is also concluded that the stiffness of shear deformable nanobeams could be reinforced at low and room temperature, while at high temperature the stiffness will be reduced.