On the Elastic Plates and Shells with Residual Surface Stresses

Recently the interest grows to development of the theory of surface elasticity with respect to nanotechnologies. Nanostructured materials demonstrate very promising properties which are different from whose of bulk materials, in general. In particular, nanosized specimens exhibit size-effect that is dependence of apparent (effective) material properties such as Young's modulus on specimen's size. One of possible explanation of these phenomena is the consideration of surface-related phenomena and their influence on the effective properties at the macroscale. In fact, surface elasticity may dramatically change effective (apparent) properties of nano- and microstructure materials. We discuss here the effective properties of thin-walled structures that are tangential and bending stiffness parameters taking into account surface/interfacial initial stresses. We consider the Gurtin-Murdoch model of surface elasticity. We show that the surface elasticity results in positive size-effect that is stiffening of nano-sized bodies in comparison with their bulk counterparts. Special attention will be paid to residual surface stresses. Unlike to surface elastic moduli there are no restrictions for values of residual stresses. In particular, we show that the compressive residual stresses may lead to negative size-effect that is to decreasing of an effective stiffness for nano-sized specimens.