Thermoelastic analysis at the nanoscale is becoming important due to the miniaturization of the device and wide application of ultrashort lasers, and the classical thermoelastic theory is no longer applicable under extreme environments, i.e. extremely high temperature gradient or heat flux, extremely short action time, and extremely small structure size. The nonlocal thermoelastic model is developed to predict the thermoelastic behavior of nanostructures under extreme environments in this paper. The governing equations with temperature-dependent thermal conductivity are solved by Kirchhoff and Laplace transformation. As a numerical example, the transient thermoelastic responses of a slab with temperature-dependent thermal conductivity are investigated. From numerical results, the effects of nonlocal parameters and the temperature-dependent thermal conductivity are discussed, systematically. The results show that the above parameters have significant effects on the transient thermoelastic responses, which is crucial to predict the thermoelastic response accurately for the design and processing of the nanostructures.

由于设备的小型化和超短激光的广泛应用，纳米尺度的热弹性分析变得越来越重要，并且经典的热弹性理论不再适用于极端环境，例如，极高的温度梯度或热通量，极短的作用时间以及极小的结构尺寸。本文建立了非局部热弹性模型来预测纳米结构在极端环境下的热弹性行为。通过基尔霍夫和拉普拉斯变换来求解与温度相关的导热系数的控制方程。作为数值示例，研究了温度依赖性导热系数的平板瞬态热弹性响应。从数值结果来看 系统地讨论了非局部参数和随温度变化的导热系数的影响。结果表明，以上参数对瞬态热弹性响应具有显着影响，这对于准确预测纳米结构的设计和加工的热弹性响应至关重要。