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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：通过广义分数热传导在功能渐变材料的裂纹条带中的瞬态热弹性响应

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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：该工作致力于分析由功能上渐变材料制成的弹性条带的热冲击问题，该弹性带含有基于广义的分数热传导理论平行于自由表面的裂缝的裂缝。假设嵌入式裂缝被绝缘。使用傅里叶变换和拉普拉斯变换来解决与时间分数偏微分方程相关的混合初始边值问题。通过求解奇异积分方程的系统来评估拉普拉斯变换域中的温度和热应力。通过应用拉普拉斯变换的数值反演来给出时域中热弹性场的数值结果。图形上示出了上下裂纹面和下裂纹面之间的温度跳跃和裂缝尖端的热应力强度因子，以及热通量，分数令和梯度指数的相位滞后在控制传热过程中起不同的作用。制作了非傅立叶模型与经典傅立叶模型之间的温度跳跃和热应力强度因子的比较。数值结果表明，波浪状行为和记忆效果是分数卡塔纳热传导的两个显着特征，其不会发生经典的傅里叶热传导。 （c）2019 Elsevier Inc.保留所有权利。

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