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首页> 外文期刊>Applied Mathematical Modelling >Transient thermoelastic response in a cracked strip of functionally graded materials via generalized fractional heat conduction
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Transient thermoelastic response in a cracked strip of functionally graded materials via generalized fractional heat conduction

机译：广义分数热传导在功能梯度材料裂纹带中的瞬态热弹性响应

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摘要

This work is devoted to analyzing a thermal shock problem of an elastic strip made of functionally graded materials containing a crack parallel to the free surface based on a generalized fractional heat conduction theory. The embedded crack is assumed to be insulated. The Fourier transform and the Laplace transform are employed to solve a mixed initial-boundary value problem associated with a time-fractional partial differential equation. Temperature and thermal stresses in the Laplace transform domain are evaluated by solving a system of singular integral equations. Numerical results of the thermoelastic fields in the time domain are given by applying a numerical inversion of the Laplace transform. The temperature jump between the upper and lower crack faces and the thermal stress intensity factors at the crack tips are illustrated graphically, and phase lags of heat flux, fractional orders, and gradient index play different roles in controlling heat transfer process. A comparison of the temperature jump and thermal stress intensity factors between the non-Fourier model and the classical Fourier model is made. Numerical results show that wave-like behavior and memory effects are two significant features of the fractional Cattaneo heat conduction, which does not occur for the classical Fourier heat conduction. (C) 2019 Elsevier Inc. All rights reserved.
机译：这项工作致力于根据广义分数热导理论分析由功能梯度材料制成的弹性条的热冲击问题，该弹性条包含平行于自由表面的裂纹。假定嵌入的裂缝是绝缘的。使用傅里叶变换和拉普拉斯变换来解决与时间分数阶偏微分方程有关的混合初边值问题。拉普拉斯变换域中的温度和热应力通过求解奇异积分方程组进行评估。通过应用拉普拉斯变换的数值反演，可以给出时域中热弹性场的数值结果。图解了上下裂纹面之间的温度跃迁以及裂纹尖端处的热应力强度因子，并且热通量的相位滞后，分数阶和梯度指数在控制传热过程中起着不同的作用。比较了非傅立叶模型和经典傅立叶模型之间的温度跃迁和热应力强度因子。数值结果表明，波浪形行为和记忆效应是分数Cattaneo热传导的两个重要特征，而经典傅里叶热传导则没有这种特征。 （C）2019 Elsevier Inc.保留所有权利。

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