摘要
A rectangular finite element for laminated plate with bonded and/or embedded piezoelectric sensors and actuators is developed based on the variational principle and the first order shear deformation theory. The element has four-node, 20-degrees-of-freedom with one potential degree of freedom for each piezoelectric layer to represent the piezoelectric behavior. The higher order derivation of deflection is obtained by using the normal rotation expressions to take the effects of transverse shear deformation into considerations. The finite element can accurately simulate the deformation of both thin and moderately thick plates. A Fortran program is written and a number of benchmark tests are exercised to verify its effectiveness. Results are compared well with the existing data. The unbalanced composite with piezoelectric layers is then analyzed by using the model. Results show that the changes of the ratio between the thickness of positive angle layers and the negative angle layers have an effect on the deformation of the structure under the same electric loading.
基于变分原理和一阶剪切理论 ,本文建立了一种新的机电耦合矩形有限单元 ,该单元具有四个节点 2 0个位移自由度 ,电自由度为单元中的压电铺层层数。通过静态控制方程推得的旋转位移表达式中含有横向位移的三次导数 ,从而该单元不仅能分析薄板的变形 ,而且还能分析中厚板在电载荷和外力载荷作用下的变形。然后 ,根据所建立的有限单元 ,结合相关方程 ,编写了有限元分析程序并对一些算例进行了数值模拟 ,通过将所得结果与有关文献的结果进行对比 ,验证了本文单元的有效性。最后对压电非均衡复合材料在电载荷作用下的变形进行了分析。结果表明 ,当复合材料中正的铺层角和对应的负铺层角的厚度比改变时 。
基金
国家自然科学基金 ( 1 0 0 72 0 2 6)资助项目
航空科学基金 ( 99B5 2 0 1 0 )资助项目~~
