A finite element formulation of a nonclassical beam theory based on the Gurtin–Murdoch model for continua with deformable elastic surfaces is presented. The governing equations for thin and thick beams are used together with a weighted residual formulation to explicitly obtain the beam stiffness and mass matrices. Numerical solutions for selected test cases are compared with the analytical results available in literature for beam static deflections, natural frequencies, and buckling loads. The modified bending stiffness corresponding to the present model agrees closely with a recently reported rigorous solution. The maximum influence of surface energy effects is observed for cantilever beams. The finite element scheme provides an efficient tool to analyze, design, and predict the mechanical response of beam elements encountered in nanoelectromechanical systems and other nanoscale devices.
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