压电复合材料层合板的热压电弹性简化模型研究

STUDY ON SIMPLIFIED THERMOPIEZOELASTIC MODEL FOR PIEZOELECTRIC COMPOSITE LAMINATES

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。

Based on the Variational Asymptotic Method （VAM）, a simplified thermopiezoelastic model for piezoelectric composite laminates under mechanical, thermal and electronic loads is presented in order to effectively formulate the originally one-way coupled thermopiezoelasticity problem. The total potential functional is deduced based on the principle of virtual work. Based on the VAM, the total potential functional is asymptotically expanded to a series of 2-D flmctional by taking advantage of the inherent small parameter. The approximate functional after dimensionality reduction is converted to a form of the Reissner model. Finally, the recovery relations for 3-D fields are provided to accurately predict the distribution of 3-D fields along the thickness direction. The results show that the 3-D field recovered by this model agrees better with the exact results than that by the First-Order Shear Deformation Theory （FOSDT） and Classic Laminated Theory （CLT）, indicating the validity of this piezoelectric composite laminates model.