A microstructure- and surface energy-dependent third-order shear deformation beam model

A new non-classical third-order shear deformation model is developed for Reddy–Levinson beams using a variational formulation based on Hamilton’s principle. A modified couple stress theory and a surface elasticity theory are employed. The equations of motion and complete boundary conditions for the beam are obtained simultaneously. The new model contains a material length scale parameter to account for the microstructure effect and three surface...