A BERNOULLI-EULER BEAM MODEL BASED ON THE LOCAL GRADIENT THEORY OF ELASTICITY

摘要

Using the total energy balance equation and principle of the frame indifference, a fundamental set of relations of the local gradient continuum model of elastic solids is formulated. The model is based on taking account of non-convective and non-diffusive mass flux related to the changes in the material microstructure. Linear stationary governing equations of the local gradient theory and corresponding boundary conditions are also derived by variational principle. In order to investigate the size-dependent behavior of nano-scale structures, this model is combined with the Bernoulli-Euler beam theory. Deflection of the cantilever beam subjected to the end-point loading under the plane stress conditions is evaluated and compared to the corresponding ones provided by the classical theory and by the strain gradient theory. It is shown that the beam deflection within the local gradient theory is smaller than that predicted by the classical Bernoulli-Euler beam theory. This work may be of special interest for designing the devices utilizing the micro/nano-beam elements.