具有固支边的功能梯度压电矩形板静力解

从三维弹性理论和压电学理论出发,通过假设满足边界条件的位移函数,推导出具有固支边的功能梯度压电板的状态方程,并运用状态变量法以及层间连续条件,在每一层端点处应用配点法,给出了满足周边和上、下表面所有边界条件的解析解。该文将状态变量法运用在具有固支边的功能梯度压电材料的静力问题上,给出了不同梯度分布压电板在具有固支边界条件下的静力解,讨论了梯度变化函数对挠度和应力场的影响,为功能梯度压电结构设计及材料优化提供一定参考依据。

Static analysis of functionally graded piezoelectric rectamgular pIates with clamped edges

Based on the theories of 3-D elasticity and piezoelectricity,the state equations of functionally graded piezoelectric rectangular plates with clamped edges are established by assuming appropriate boundary functions.By the state vector method,analytical solutions that satisfy all the boundary conditions at four edges as well as upper and bottom surfaces are presented.The significance of this paper is to apply the static vector method in the static analysis of functionally graded piezoelectric rectangular plates with clamped edges.The effects of the different functionally gradient material models on the displacement and the stress field are discussed.The results can provide references for functionally graded piezoelectric structure design and materials optimization.