Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates

We use the principle of virtual work to derive a higher-order shear and normal deformable theory for a plate comprised of a linear elastic incompressible anisotropic material. The theory does not use a shear correction factor and employs three components of displacement and the hydrostatic pressure as independent variables. For a Kth order plate theory, a set of 4(K + 1) coupled equations need to be solved. for the (K + 1) pressures and the 3(K + 1) displacements defined oil the reference surface of the plate. Equations for free vibrations of a plate are derived, and equations for the determination of frequencies and the corresponding mode shapes of a simply supported rectangular plate are given. (c) 2007 Elsevier Ltd. All rights reserved.