Three-dimensional analysis of piezocomposite plates with arbitrary geometry and boundary conditions

Two-dimensional piezoelectricity. Part I: eigensolutions of nondegenerate and degenerate materials

“…In most works on piezoelectricity (Tiersten, 1969;Wang and Zheng, 1995;Sosa and Castro, 1994;Bisegna and Maceri, 1996;Ding et al, 1996;Heyliger, 1997;Vel and Batra, 2000;Shodja and Kamali, 2003), the primary unknown variables are taken to be the displacements and the electric field. The constitutive matrix used in such theories is the inverse matrix of [-], since the roles of the primary and secondary unknown variables are reversed.…”

“…The constitutive equations of linear piezoelectricity are well known. Based on these equations, a number of three-dimensional and two-dimensional solutions for piezoelectric materials (Sosa, 1991;Pak, 1992;Sosa and Castro, 1994;Suo et al, 1992;Ruan et al, 1999;Shodja and Kamali, 2003), and homogeneous or multilayered piezoelectric plates have been obtained (Ray et al, 1992;Mitchell and Reddy, 1995;Bisegna and Maceri, 1996;Huang and Wu, 1996;Heyliger, 1997;Vel and Batra, 1999). Nevertheless, the subject has not been as fully developed, in an analytical sense, as anisotropic elasticity.…”

Elastic/piezoelectric solids with electro-mechanical singular surfaces

“…Note that the displacements and electric potential appear in (20) and (21), whereas (22) and (23) are in terms of their gradients. If S is the whole external boundary…”

“…The proposed approach entails exact satisfaction of the kinematic boundary conditions (20), (21), and (26), and accurately accounts for the boundary conditions (22), (23), (27), and (28), which involve the gradients of the displacements and electric potential.…”

“…Except for the work of Vel and Batra [26] who employ Eshelby-Stroh formalism and consider various types of boundary condition, all the above mentioned contributions address simply supported type boundary conditions only. Static analysis of piezocomposite plates with complex geometries and non-planar boundaries are given by Shodja and Kamali [23] and Kamali and Shodja [14]. As far as the analytical methods for treatment of vibrations of piezoelectric plates are concerned the works of Vel et al [27], Heyliger and Brooks [8], and Heyliger and Saravanos [10], and in the case of elastic plates the works of Jones [12,13] and Sirinivas [24], and Sirinivas and Rao [25] should be mentioned.…”