In order to overcome the disadvantage that it is inconvenient to introduce stress boundary conditions when solving the stress of element nodes in displacement finite element method

firstly

according to the generalized minimum potential energyprinciple of piezoelectric materials

a practical 8-node hexahedral nonconforming displacement element is proposed for the static analysis of piezoelectric structures. Then

based on the generalized H-R variational principle

a linear equations method for calculating the generalized stress of composite structures with piezoelectric layers is proposed. This method provides conditions for the introduction of generalized stress boundary conditions

and ensures the continuity of stress on the same node of adjacent elements

which lays a theoretical foundation for high-precision numerical results. Numerical results show that the accuracy of generalized stress results obtained by linear equations method is higher than that by Gauss-point stress extrapolation method(GSEM).