压电复合材料层板柱面弯曲的精化理论

本研究旨在建立精确的压电复合材料层板理论。位移场和电势场采用近似表达，其沿板厚的分布通过构造高精度的位移分布函数和电势分布函数来描述。这两个函数由三雏弹性平衡方程和静电平衡方程的特解来导出，从而满足复杂的力电耦合关系和各类连续条件，保证了本文理论的高精度。本文理论仅涉及4个位移和电势变量，且不随层数的增加而增多，较之变量随层数而增多的分层理论简单得多，平衡方程形式简单；也便于发展成有限元等数值模型。通过与三维精确解比较，算例显示了本文理论的高精度和有效性。

Accwrate Theory of Laminated Piezoelectric Composite Plates under Cylindrical Bending

An accurate theory of laminated piezoelectric composite plates in cylindrical bending is developed. The displacement field and electric potential field are depicted approximately by the accurate displacement and electric potential distribution functions through thickness, respectively. The two functions are formulated according to the particular solutions to the three dimensional elasticity equilibrium equation and electrostatics charge equation. Hence, the complicated electromechanical relations and interfacial continuity conditions are satisfied and the higher accuracy of the present theory is ensured. This theory involves only 4 displacement and electric potential variables and the number is independent of the number of layers. This theory is much simpler than layerwise theories and results in a simpler form of the equilibrium equation, furthermore it is more suitable for formulation of a corresponding finite element model. The high accuracy and effectiveness of this theory is demonstrated in numerical examples compared with the three dimensional exact solutions.