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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 a six-degree-of-freedom displacement field and potential field, the governing equations of piezoelectric composite laminates are established. Under simple support boundary conditions, the analytical solution of orthogonal rectangular piezoelectric composite laminates is obtained. The theory is an equivalent single-level theory, the control equation of the variable is only six, and does not change with the number of layers, so that the mathematical solution of the solution simple. In this theory, the displacement distribution function and the potential distribution function that determine the accuracy are determined by the special solutions of the three-dimensional stress and electrostatic equilibrium equations so as to satisfy the continuity condition of the piezoelectric laminate and the surface force and the electrical conditions. The example verifies the high accuracy of the equivalent monolayer theory in this paper.