A microscale beam theory considering surface effect based on the state space method

Development of MEMS/NEMS leads to much academic attention paid on the nanoscale structures. The mechanical behavior of these nanoscale structures should be understood in detail for the sake of design and manufacture of MEMS/NEMS. Unlike the common structures at macroscale, size effect usually plays a significant role in nanoscale structures which has been found in many experimental studies and numerical simulations. Therefore, the surface effect must be considered for the analysis of materials and structures at nanoscale. This work proposed a new microscale beam theory based on the state space method and variational principle of mixed energy in Hamiltonian system. The surface stresses are related to the bulk stresses and displacements by the state equations. The equilibrium equations of the stress resultants are derived through the stationary condition of the mixed energy as well as the constitutive relation between the shear force and displacements. Finally, a numerical example illustrates the proposed theory.