A novel beam model suitable at the microscale

A novel beam model is proposed to address the limitations of existing microscale beam models by introducing a higher-order displacement field assumption for the modified couple stress theory. The governing equations and boundary conditions are derived using the variational principle. Validation through finite element analysis for a simply supported beam problem demonstrates the beam model successfully captures the width-dependent behavior of microbeams, which existing beam models cannot explain. Additionally, the beam model accurately represents the plane strain behavior as the beam width increases and the classical beam behavior at a small length scale parameter.