In a series of recent papers we have shown how the continuum mechanics can be extended to nano-scale by supplementing the equations of elasticity for the bulk material with the generalised Young-Laplace equations of surface elasticity. This review paper begins with the generalised Young-Laplace equations. It then generalises the classical Eshelby formalism to nano-inhomogeneities; the Eshelby tensor now depends on the size of the inhomogeneity and the location of the material point in it. The generalized Eshelby formalism for nano-inhomogeneities is then used to calculate the strain fields in quantum dot (QD) structures. This is followed by generalisation of the micro-mechanical framework for determining the effective elastic properties of heterogeneous solids containing nano-inhomogeneities. It is shown that the elastic constants of nanochannel-array materials with a large surface area can be made to exceed those of the non-porous matrices through pore surface modification or coating. Finally, the scaling laws governing the properties of nano-structured materials are given.
In this paper a scaling approach for the solution of 2D FE models of electric machines is proposed. This allows a geometrical and stator and rotor resistance scaling as well as a rewinding of a squirrel cage induction machine enabling an efficient numerical optimization. The 2D FEM solutions of a reference machine are calculated by a model based hybrid numeric induction machine simulation approach. In contrast to already known scaling procedures for synchronous machines the FEM solutions of the induction machine are scaled in the stator-current-rotor-frequency-plane and then transformed to the torque- speed-map. This gives the possibility to use a new time scaling factor that is necessary to keep a constant field distribution. The scaling procedure is validated by the finite element method and used in a numerical optimization process for the sizing of an electric vehicle traction drive considering the gear ratio. The results show that the scaling procedure is very accurate, computational very efficient and suitable for the use in machine design optimization.