Thermoelastic analysis of nanobar based on nonlocal integral elasticity and nonlocal integral heat conduction

Abstract

The thermoelastic analysis is extremely important due to the highly integrated characteristics in micro- and nano-electro-mechanical systems. In this paper, thermal flux driven (TFD) and temperature gradient driven (TGD) two-phase local/nonlocal heat conduction integral models (NHCIM) are developed to describe size-dependent heat conduction. Combining TFD- and TGD-NHCIMs with strain- and stress-driven two-phase local/nonlocal elastic integral models, four types of nonlocal thermoelastic integral models are developed to predict the thermoelastic behavior of microstructures. The nonlocal thermoelastic integral models are applied to analyze the thermoelastic behavior of clamped-clamped microrod with prescribed boundary temperature and heat flux for each end. Analytical solutions for the distribution of temperature, displacement and thermal stresses are derived and expressed explicitly with several unknown constants, which can be determined by the standard and constitutive boundary conditions. The effects of nonlocal parameters on the distribution of temperature, displacement and thermal stress are investigated numerically and systematically. The numerical results show that nonlocal thermoelastic models based on the combination between strain- and stress-driven two-phase local/nonlocal elastic models respectively with TGD- and TFD-NHCIMs would lead to consistent size-dependent response when increasing the elastic and thermal nonlocal length-scale parameters at the same time, while those based on the combination between strain- and stress-driven two-phase nonlocal elastic models respectively with TFD- and TGD-NHCIMs would lead to inconsistent prediction.

Keywords:

• Consistency
• nonlocal integral elasticity
• nonlocal integral heat conduction
• nonlocal thermoelasticity
• size effects

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (No.12172169) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Zhang appreciates the support of the China Scholarship Council (CSC).