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.

摘要

由于微和纳米机电系统的高度集成特性，热弹性分析非常重要。在本文中，开发了热通量驱动 (TFD) 和温度梯度驱动 (TGD) 两相局部/非局部热传导积分模型 (NHCIM) 来描述与尺寸相关的热传导。将 TFD 和 TGD-NHCIM 与应变和应力驱动的两相局部/非局部弹性积分模型相结合，开发了四种类型的非局部热弹性积分模型来预测微结构的热弹性行为。应用非局部热弹性积分模型来分析具有指定边界温度和每端热通量的夹钳微棒的热弹性行为。温度分布的解析解，位移和热应力是用几个未知常数导出和明确表达的，这些常数可以由标准和本构边界条件确定。数值和系统地研究了非局部参数对温度、位移和热应力分布的影响。数值结果表明，基于应变驱动和应力驱动的两相局部/非局部弹性模型分别与 TGD 和 TFD-NHCIM 相结合的非局部热弹性模型将在增加弹性和热非局部时导致一致的尺寸相关响应。长度尺度参数，而那些基于应变驱动和应力驱动的两相非局部弹性模型分别与 TFD-和 TGD-NHCIM 相结合的模型将导致预测不一致。