Molecular mechanics has been widely used to analytically study mechanical behaviour of carbon nanotubes. However, explicit expressions for elastic properties of carbon nanotubes are so far confined to some special cases due to the lack of fully constructed governing equations for the molecular mechanics model. In this paper, governing equations for an analytical molecular mechanics model are fully established. The explicit expressions for five in-plane elastic properties of a chiral single-walled carbon nanotube are derived, which make properties at different length-scales directly connected. The effects of tube chirality and tube diameter are investigated. In particular, the present results show that the classic relationship from the isotropic elastic theory of continuum mechanics between Young's modulus and shear modulus of a single-walled carbon nanotube is not retained. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and also useful to the topic of linking molecular mechanics with continuum mechanics.

An analytical molecular mechanics model is established to relate the chirality- and size-dependent elastic properties of a single-walled carbon nanotube to its atomic structure. Properties at different length scales are directly connected by the derived closed-form expressions. The effects of tube chirality and tube diameter are investigated. The present analytical results are helpful to the understanding of elastic properties of carbon nanotubes, and thus are important for the application of carbon nanotubes as building blocks of nanomechanical devices.

Based on a molecular mechanics concept, a nonlinear stick-spiral model is developed to investigate the mechanical behavior of single-walled carbon nanotubes ͑SWCNTs͒. The model is capable of predicting not only the initial elastic properties ͑e.g., Young's modulus͒ but also the stress-strain relations of a SWCNT under axial, radial, and torsion conditions. The elastic properties, ultimate stress, and failure strain under various loading conditions are discussed and special attention has been paid to the effects of the tube chirality and tube size. Some unique mechanical behaviors of chiral SWCNTs, such as axial strain-induced torsion, circumferential strain-induced torsion, and shear strain-induced extension are also studied. The predicted results from the present model are in good agreement with existing data, but very little computational cost is needed to yield them.

Flapping-wing devices working in an energy-harvesting mode have the advantage of environmental adaptation. To analyze the energy-extraction characteristics of a flapping wing with the free-surface effect, transient-numerical studies were carried out based on the homogeneous two-phase volume-of-flow model, the shear stress transport k–ω turbulence model, and dynamic-grid technology. These studies took into consideration the influences of the dimensionless submergence depth Sd along with the Froude number Fr. The following results were obtained. (1) In the subcritical condition of Fr < 1, there was a critical hydrofoil submergence depth. When it was greater than this critical value, the existence of the free surface was able to promote the energy-extraction efficiency. On the contrary, the closer the flapping wing was to the free surface, the lower its energy-harvesting efficiency was. (2) When the hydrofoil submergence depth was small, the energy-harvesting efficiency first increased and then decreased with the increase in Fr. Furthermore, the smaller Sd was, the faster the energy-extraction efficiency of the flapping wing decreased. While Sd was large, for example Sd > 9, the energy-extraction efficiency first increased and then gradually approached the unbounded-flow condition as Fr increased, but it was always lower than the unbounded-flow case. (3) Compared with the case of unbounded flow, the existence of the free surface affected the motion of the leading-edge vortex, thereby changing the magnitude and direction of the lift force and pitch moment. The relative position of the free-surface wave crest to the wing also affected the pressure distribution around the flapping-wing surface, which in turn affected the energy-harvesting properties. Additionally, Fr affected the formation and shedding of the vortex around the flapping wing, and the movement synchronization between the leading-edge vortex and the flapping wing was extremely important to the energy-harvesting performance.

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