电–热–力载下BNNTs增强压电板的非线性弯曲
Nonlinear Bending of Piezoelectric Plate Reinforced with BNNTs under ElectroqThermo-Mechanical Loading
摘要: 本文基于非线性应变几何关系、温度效应和压电理论，研究了电–热–力耦合作用下硼氮纳米管(BNNTs)增强压电板的非线性弯曲，并建立了硼氮纳米管增强压电板的本构关系。通过变分法，推导出结构的非线性控制方程。用差分离散和迭代法进行求解。算例中详细讨论了体积比、温度、电压以及荷载等因素对BNNTs增强压电板非线性弯曲的影响。结果表明板在线性情况下的挠度和弯矩大于非线性；当横向荷载Q增大时，非线性效应增强；对BNNTs施加正负电压会导致挠度和弯矩的增加和减少；而且挠度和弯矩随着温度的升高而增大，也会随着基体中BNNTs体积分数的增加而减小。
Abstract: Based on the nonlinear strain geometry relationship, temperature effect and piezoelectric theory, it is studied the nonlinear bending of boron nitride nanotube (BNNTs) reinforced piezoelectric plate under the action of electro thermal force in this paper. And the constitutive relation of boron nitride nanotube reinforced piezoelectric plate is established. The nonlinear control equation of the structure is derived by the variational method. The difference method is used to disperse, and then it is used to solve the problem by the iterative method. In this calculation, the effects of the volume ratio, temperature, voltage and load on the nonlinear bending of the BNNTs reinforced piezoelectric plate are discussed in detail. The results show that the deflection and bending moment of the plate in the linear case are greater than those in the case of the nonlinear case. When the transverse load Q increased, the nonlinear effect increased. Applying positive and negative voltage to BNNTs will cause the increase and decrease of deflection and bending moment. With the increase of temperature the deflection and bending moment increase, and with the volume fraction of BNNTs in the matrix they will also decrease.
文章引用：杨金花, 周涛. 电–热–力载下BNNTs增强压电板的非线性弯曲[J]. 材料科学, 2018, 8(6): 742-751. https://doi.org/10.12677/MS.2018.86088

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