Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms

Simple closed-form analytic solutions have been obtained for the effect of initial residual stress on the bending stiffness of a symmetric trilayer plate/beam and for the combined effect of surface elasticity and initial surface stress on the bending stiffness of a nanofilm/nanobeam.The relative effect of the initial residual stress is generally limited to the range of the material yield strain.For nanofilms and nanobeams, the effect of the surface elasticity reduces with an increase in the thickness, but the initial surface stress effect can be retained at a constant level of up to the limit of elastic strain if it can be controlled, for example by the application of an electrical potential.