Based on the pyroelectricity, piezoelectricity, and thermoelasticity in nonlinear constitutive equations, we report a thermal piezoelectric semiconductor model under a mechanical load, a Schottky contact boundary condition, and a temperature gradient. To solve this nonlinear boundary value problem, we propose a shooting method. In comparison with the results obtained by COMSOL, the shooting method is reliable. Furthermore, the influence of the temperature gradient on the extended displacements and stress fields is discussed. The numerical results show that a small change in the temperature has the remarkable effect on a mechanical electric field in thermal piezoelectric semiconductors.

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热压电半导体板中非线性边值问题的解决方法

基于非线性本构方程中的热电，压电和热弹性，我们报告了在机械载荷，肖特基接触边界条件和温度梯度下的热压电半导体模型。为了解决这个非线性边值问题，我们提出了一种射击方法。与COMSOL获得的结果相比，该射击方法是可靠的。此外，讨论了温度梯度对扩展位移和应力场的影响。数值结果表明，温度的微小变化对热压电半导体中的机械电场具有显着影响。