基于Legendre多项式的双压电层合板三维压电谱元法模拟

Numerical simulation of piezoelectric bimorphs using three dimensional piezoelectric spectral element method based on Legendre polynomial

谱单元作为一种高阶单元具有计算效率高和精度高的特点。本文在基于Legendre正交多项式的三维谱单元基础上提出了三维压电谱单元模型,用于压电层合板静力和动力性能模拟研究。压电层合板结构中的位移和电势自由度均离散到三维压电谱单元Gauss-Lobatto-Legendre(GLL)配置节点上,并且未对电势沿压电层厚度方向上的变化做任何假定。通过提高谱单元中沿压电层合板厚度方向上的形函数阶数的方法,来削弱三维谱单元在模拟薄板结构中出现的剪切闭锁现象。为验证单元的计算精度,取双压电层合板结构进行静力和动力行为模拟验证,并将计算结果与现有文献中的其它单元模型及有限元结果进行对比。结果表明,压电谱单元可有效模拟压电层合板的静力和动力行为,且提高谱单元形函数阶数可提高数值模拟精度。

As a high order element type,the spectral element has the characteristics of high efficiency and precision.In this paper,a three dimensional(3D)piezoelectric spectral element model is proposed based on spectral element formed with Legendre orthogonal polynomial to simulate the static and dynamic behavior of piezoelectric laminated composite plate.In a piezoelectric laminated composite plate,both the unknown mechanical displacement and electric potential freedoms are discretized at Gauss-Lobatto-Legendre(GLL)points of piezoelectric spectral element and no hypothesis is made on the electric potential variation across the thickness of the piezoelectric layers.The order of the shape function through-the-thickness of piezoelectric plate in piezoelectric spectral element is increased to weaken the effect of shear locking for the 3D element simulating thin plate structures.In order to verify the precision of the proposed element model,static and dynamic models of piezoelectric bimorphs are analyzed and the simulated results are compared with those calculated by other element models from literatures and finite element models.Results showed that piezoelectric spectral element model is efficient in simulating the behavior of piezoelectric laminated composite plate structures and developing the order of the shape function in spectral element can improve the simulation accuracy.