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为有效分析压电复合材料层合板在热、电和载荷下的单向耦合热电弹性问题,基于变分渐近方法(VAM)建立热电弹性简化模型。首先根据虚功原理推导三维压电复合板总势能泛函。然后基于变分渐近法,利用板固有的小参数将三维总势能泛函渐近扩展为系列二维泛函,同时将近似泛函转换为Reissner形式以便实际工程应用。最后建立三维场重构关系以正确预测沿厚度方向的应力分布。计算结果显示:基于该模型重构的沿厚度方向横向剪切应力较古典层合理论和一阶剪切变形理论精确度更好,与三维有限元精确解相一致,表明该模型在压电复合材料层合板应力预测上的有效性。
In order to effectively analyze the one-way coupled thermoelectroelasticity of piezoelectric composite laminates under heat, electricity and load, a simplified thermoelastic model is established based on the Variational Asymptotic Method (VAM). According to the principle of virtual work, the general potential energy function of 3D piezoelectric composite plate is derived first. Then, based on the variational asymptotic method, the three-dimensional general potential functional is extended as a series of two-dimensional functional by using the small intrinsic parameter of the plate, and the approximate functional is transformed into Reissner form for practical engineering application. Finally, the reconstruction of three-dimensional field to establish the relationship between the correct prediction of the stress distribution along the thickness direction. The calculated results show that the transverse shear stress along the thickness direction reconstructed based on the model is more accurate than the classical laminar shear theory and the first-order shear deformation theory, which is consistent with the exact solution of the three-dimensional finite element method. The effectiveness of material laminates in stress prediction.