A Discrete-Layer Model of Laminated Hygrothermopiezoelectric Plates

The steady-state and transient behavior of laminated hygrothermopiezoelectric plates is studied under the coupled effects of mechanical, electrical, thermal, and moisture fields. A three-dimensional discrete-layer model is developed for analyzing rectangular multilayered laminated plates with various types of boundary condition. Excitations on the laminates are specified as surface traction, electric potential, temperature, and/or moisture concentration on top, interlaminar, and bottom surfaces. The discrete-layer model employs one-dimensional finite-element approximations in the through-thickness direction and two-dimensional in-plane analytical functions (e.g., trigonometric and polynomial functions). The transient problem is formulated in a standard matrix form and then solved by direct step-by-step integration using the Newmark beta method. Numerical examples are demonstrated for problems of simply supported conditions and for hygrothermal diffusion in an infinite plate. The discrete-layer model is verified by comparing with available exact solutions, and also some new results are presented.