压电复合材料正交层板的精确理论

Accurate theory for cross-ply piezoelectric composite laminates

基于一个六自由度的位移场和电势场,建立了压电复合材料层板的控制方程。在简支边界条件下,得到了正交矩形压电复合材料层板的解析解。该理论是一个等效单层理论,控制方程的变量仅六个,且不随层数变化,使解的数学过程简洁。在该理论中,决定精度的位移分布函数和电势分布函数由三维应力和静电平衡方程的特解来确定,使之满足压电层板界面连续条件与板面力及电条件。算例验证了本文中等效单层理论的高精度。

Based on the displacement and potential fields with six degrees of freedom,the equations of motion for piezoelectric composite laminates were established.The closed solutions for cross-ply rectangular piezoelectric composite laminates with simply-supported boundaries are obtained.The present theory is an equivalent single layer theory and contains only six displacement and electric variables,the number of which is independent of the layers.The equations of motion can be solved simply.The displacement and electric potential fields are depicted by the displacement and electric potential distribution functions through thickness,respectively.The three functions are formulated according to particular solutions to the three-dimensional elasticity equilibrium equations and electrostatics charge equation by enforcing interfacial continuity conditions and force and electric conditions at the top and bottom surfaces.The high accuracy of this equivalent single layer theory is demonstrated in the numerical examples.