A new Bernoulli–Euler beam model based on a reformulated strain gradient elasticity theory

A new non-classical Bernoulli–Euler beam model is developed using a reformulated strain gradient elasticity theory that incorporates both couple stress and strain gradient effects. This reformulated theory is first derived from Form I of Mindlin’s general strain gradient elasticity theory. It is then applied to develop the model for Bernoulli–Euler beams through a variational formulation based on Hamilton’s principle, which leads to the...