Thermo-mechanical properties of one-dimensional nanostructures based on nonlocal elasticity theory

Abstract

Nanostructures including nanobeams, nanorods, nanotubes etc., have attracted worldwide attention for its potential applications in many areas of science and engineering. In addition, these structures may experience high temperature and thermal loads during synthesis, fabrication and operation. This makes it important to have a good knowledge of the thermal properties of nanostructures. Based on Euler-Bernoulli beam model, Timoshenko beam model and Eringen’s nonlocal elasticity theory, exact nonlocal Euler-Bernoulli beam (ENE) model and exact nonlocal Timoshenko beam (ENT) model considering linear and nonlinear strain-displacement relation are established in this thesis. Subsequently, by combining the ENE and ENT models with thermal elasticity theory, the nonlocal thermoelastic models are set up to investigate the thermal mechanical properties of one-dimensional nanostructures including thermal bending, thermal buckling, thermal vibration and wave propagation. By considering the ENE model with linear strain-displacement relation, the linear bending of nanobeam under temperature field is studied first. The thermal effects of typical nanobeams are presented where new exact, analytical solutions with physical boundary conditions are derived. Moreover, the critical temperature change of nanobeam due to the combination of transverse load and axial load are obtained. Based on the same model, the effect of nanoscale and temperature change on wave propagation in nanotube is investigated. The spectrum relation between wave frequency and wave number with thermal effect is obtained. Then the ENE model considering nonlinear strain-displacement relation is applied on the nonlinear buckling analysis of nanorod including temperature. The analytical solution for critical buckling load and critical temperature change of Euler-Bernoulli nanorod are presented. The nonlinear free vibration of nanorod with thermal effect is studied to illustrate the effect of nonlocal nanoscale and temperature change. The differential quadrature method (DQM) is then used to discretize the nonlinear governing equations and numerical solutions for linear and nonlinear frequencies are obtained. All results confirm the stiffness enhancement of nanobeam/nanotube/nanorod contributed by nonlocal effect. It is also concluded that the stiffness of nanobeam/nanotube/nanorod could be reinforced at low and room temperature, while at high temperature the stiffness will be reduced. Besides the ENE model, the ENT model with shear deformation effect considering linear strain-displacement relation is also applied to study the linear thermal bending of nanobeams and wave propagation in nanotube. The differential equations of equilibrium both for transverse deflection and transverse rotation with boundary conditions are obtained. The spectrum relation between wave frequency and wave number with thermal effect is also obtained. The nonlinear thermal bending analysis of nanobeams is presented based on the ENT model with nonlinear strain-displacement relation. The analytical solution of transverse deflection and rotation of nanobeam with thermal effect is obtained. This model is also used in nonlinear thermal buckling for a shear deformable nanocolumn. A parametric study is conducted in the above-mentioned cases to analyze the effects of nonlocal nanoscale, temperature change, shear deformation and von Kármán nonlinearity for bending, buckling and wave propagation of nanobeam/nanocolumn/nanotube under temperature field. It is observed that these factors have great influence on the thermal mechanical properties of nanobeam/nanocolumn/nanotube. Similar results with respect to the ENE model are also obtained with stiffness enhancement of nanostructures, that is, lower transverse deflection, higher wave frequency and larger critical buckling load. It is also found that increasing the value of temperature change makes the nanobeam/nanocolumn/nanotube stiffer and softer corresponding to low and high temperature environment conditions, respectively. The results confirmed that nanobeam/nanocolumn/nanotube stiffness is reduced due to shear deformation and enhanced by Von Kármán nonlinearity. It is also concluded that the critical temperature change is increased with larger diameter to length ratio and higher nonlocal nanoscale. In conclusion, thermal mechanical properties based on ENE model and ENT model with thermal effect considering linear and nonlinear strain-displacement relation are investigates in this thesis. The results reported in this thesis are expected to be useful for designing micro- or nano-electromechanical systems (MEMS or NEMS) and some other nanoscale devices using nanobeam-like structures.

Date of Award	16 Jul 2012
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	C W LIM (Supervisor)