Acta Mech. Sin. DOI 10.1007/s10409-016-0559-1 RESEARCH PAPER Stress analysis of thermally affected rotating nanoshafts with varying material properties Keivan Kiani 1 Received: 24 October 2015 / Revised: 23 December 2015 / Accepted: 4 January 2016 © The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2016 Abstract Based on the surface elasticity theory of Gurtin- Murdoch, thermo-elastic fields within rotating nanoshafts with varying material properties subjected to a thermal field are explicitly examined. Accounting for the surface energy effect, the nonclassical boundary conditions are enforced in the cases of fixed-free and free-free conditions. The effects of variation of material properties, temperature of the envi- ronment, angular velocity, and radius of the outer radius on the radial displacement, hoop and radial stresses are investi- gated. In all performed studies, the role of the surface effect on the thermo-elastic field of the nanostructure is methodi- cally discussed. Keywords Rotating nanoshaft · Thermo-elastic field · Surface energy effect · Non-classical boundary conditions · Analytical modeling 1 Introduction The advancement of noncontact methods to rotate nanorods, nanowires and nanotubes is of great significance for exploita- tion of them as main members of the upcoming nanomotors. There is much evidence regarding rotation of micronee- dles [1], asymmetric nanorods [2], octapolar metal nanopar- ticles [3], nanowires [4], and nanotube bundles [5] by application of light or focused laser beams. In fact, these achievements of scientists have opened new horizons for B Keivan Kiani k_kiani@kntu.ac.ir; keivankiani@yahoo.com 1 Department of Civil Engineering, K.N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran fabrication of nanomachines that operate with continu- ous rotational motion. Since these nanometer-sized rotary motors do not required mechanical contact and electrical wires, a wide range of applications can be imagined for them from medicine to manufacturing. For example, these nanomachines can be used as fluid pumpers in microfluidic chips [6, 7] and nanotweezers [8, 9]. However, many exper- iments have been reported for such nanorotors, but their mechanical analyses have not yet been performed. To bridge this scientific gap, herein, we focus on elastic deformation and stresses resulting from rotational motion of a nanoshaft in a thermal environment. For structures with dimensions at the nanoscale, the ratio of the surface area to the bulk volume is much greater than the macrostructures. It indicates that if the nanos- tructure is acted upon by external loads, the ratio of the elastic strain energy of the surface layer to that of the bulk would be noticeable and such a fact should be appropri- ately considered in modeling of the nanostructure. One of the most famous surface elasticity models is that devel- oped by Gurtin and Murdoch [10–12]. In the context of such a theory, the surface layer is one of two major con- stituents of the nanostructure whose thickness is negligible. This layer is tightly attached to the underlying bulk zone. Since no slippage is allowed at the interface of the sur- face layer and the bulk zone, the displacements of the surface layer are exactly the same as those of the bulk at the vicinity of the surface. The mechanical behavior of the surface layer is completely different from that of the bulk. This leads to a new configuration of the constitutive relations, which are rationally elucidated by the theory of surface elasticity of Gurtin-Murdoch [10–12]. Actually, the surface stresses are related to the surface strains by defin- ing three crucial properties for the surface layer (i.e., two 123