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Hygrothermal stresses in one-dimensional functionally graded piezoelectric media in constant magnetic field

机译：恒定磁场中一维功能梯度压电介质的湿热应力

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摘要

This paper presents analytical solutions for hygrothermal stresses in one-dimensional functionally graded piezoelectric media. The media are subjected to an external constant magnetic field and could be rested on a Winkler-type elastic foundation. The material properties are assumed to vary through the thickness according to a power-law with different non-homogeneity indices. The governing equations including the Lorentz force effect are written in a unified form that can be used for one-dimensional functionally graded piezoelectric media in Cartesian, cylindrical, and spherical coordinates. The moisture concentration and temperature distributions along the thickness of one-dimensional media are achieved by solving the steady state Fickian moisture diffusion and Fourier heat conduction equations. The two coupled ordinary differential equations in terms of displacement and electric potential are solved analytically. The numerical results illustrate the effects of hygrothermal loading, medium geometry, non-homogeneity indices, external magnetic field, and elastic foundation on the behavior of one-dimensional piezoelectric media. For a uniform temperature rise, the influence of temperature-dependency of material properties on the electromechanical responses is investigated as well. At last, the results are verified with those reported in the literature.
机译：本文提出了一维功能梯度压电介质中湿热应力的解析解。介质受到外部恒定磁场的影响，可以放在Winkler型弹性基础上。假定材料特性根据具有不同非均匀性指数的幂律在整个厚度范围内变化。包括洛伦兹力效应的控制方程式以统一形式编写，可用于笛卡尔坐标，圆柱坐标和球坐标中的一维功能梯度压电介质。通过求解稳态Fickian水分扩散和傅里叶热传导方程，可以实现沿一维介质厚度分布的水分浓度和温度分布。用位移和电势分析了两个耦合的常微分方程。数值结果说明了湿热负荷，介质几何形状，非均匀性指数，外部磁场和弹性基础对一维压电介质行为的影响。对于均匀的温度上升，还研究了材料特性的温度相关性对机电响应的影响。最后，结果与文献报道相符。

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