3D stress analysis of generally laminated piezoelectric plates with electromechanical coupling effects
The paper examines the influence of the electromechanical coupling on the inter-laminar stresses and electric field strength near the free edges of a rectangular piezoelectric plate subjected to a constant axial displacement. After a careful review of the pertinent literatures, the governing static equations and the boundary conditions are derived for the laminated piezoelectric plate using the principle of minimum total potential energy in Cartesian coordinates. The displacements and tractions are assumed to be continuous across the perfectly bonded interfaces. A three-dimensional multi-term extended Kantorovich method is chosen to investigate numerically the influence of coupling on the free edge effect. The electromechanical coupling is examined for different two-dimensional laminates. Special coupled and uncoupled inter-laminar stress components of the piezoelectric plate are considered and the convergence of solutions are discussed. The results are compared with the available analytical results in the literature. In brief, the fundamental static equations are developed for the piezoelectric plate with a linearly increasing uniaxial displacement by tacitly assuming the internal consistency (i.e., existence and uniqueness) of solutions in rectangular Cartesian coordinates. To conclude, the paper is recommendable to everyone who is already working on structural elements of smart materials in Cartesian, rectangular Cartesian and orthogonal coordinates.
scientific article; zbMATH DE number 7187187
scientific article