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This paper presents fundamental solutions of an anisotropic elastic thin plate within the context of the Kirchhoff theory. The plate material is inhomogeneous in the thickness direction. Two systems of problems with non-self-equilibrated loads are solved. The first is concerned with in-plane concentrated forces and moments and in-plane discontinuous displacements and slopes, and the second with transverse concentrated forces. Exact closed-form Green's functions for infinite and semi-infinite plates are obtained using the recently established octet formalism by the authors for coupled stretching and bending deformations of a plate. The Green functions for an infinite plate and the surface Green functions for a semi-infinite plate are presented in a real form. The hoop stress resultants are also presented in a real form for a semi-infinite plate. [DOI: 10.1115/1.1533806]

A smart functionally graded plate consists of a plate made of a functionally gradient material and actuators made of an active material. The active material a layer or set of patches, is bonded on the metal-rich surface of the functionally graded plate. When the ceramic-rich surface of the substrate is subjected to thermomechanical loadings, displacements, and stresses may be controlled, and vibration amplitudes may be suppressed by the actuators with supplied electric power. In the attempt towards a basic understanding of the new type of smart structural system, this study considers a benchmark problem, namely, the bending of a functionally graded rectangular plate with an attached piezoelectric actuator. The transfer matrix and asymptotic expansion techniques are employed to obtain a three-dimensional asymptotic solution. In numerical computations, the locally effective material properties of the functionally gradient material are estimated by the Mori-Tanaka scheme. The three-dimensional distributions of displacements and stresses for different volume fractions of the ceramic and metallic constituents could serve as benchmark results to assess approximate theories and numerical methods.

Hu's method has been used on Reddy's third-order laminated plate theory so that the relationship between deflections of the classical and shear deformation laminated plate theories can be assessed. Results indicate that an exact differential relationship can be established with both theories. Solutions for the first-order shear deformation of laminated plates are given in terms of Kirchoff's deflection of the classical theory.