A three-component volume coordinate system generalized mixed element for piezoelectric composite structures

This paper combines the three-component volume coordinate system with the non-conforming generalized mixed element to develop an element for analyzing the static characteristics of piezoelectric composite structures. The element adopts volume coordinates as local coordinates, significantly alleviating the ill-conditioned relationship between local and Cartesian coordinates in traditional isoparametric elements under mesh distortion, thus reducing the sensitivity of the element to mesh distortion. Furthermore, the calculation of the Jacobian inverse matrix is avoided. On the other hand, this element retains the advantage of the mixed method that enables the concurrent consideration of displacement and stress boundary conditions, thereby facilitating an objective and rational description of the finite element model. Additionally, the discontinuity of in-plane stresses between layers is resolved by using a partial mixed method to separately solve the in-plane and out-of-plane stresses. Numerical examples demonstrate that the proposed element has excellent performance in the analysis of piezoelectric composite structures.