In this paper, the interface crack problems of a multilayered anisotropic medium under a state of generalized plane deformation are considered within the framework of anisotropic theory. A general solution procedure is introduced such that it can be uniformly applied to media with transversely isotropic, ortho-tropic, monoclinic, etc. layers. The problem is reduced to the solution of a system of singular integral equations by means of Fourier transform method and the stiffness matrix formulation. A Jacobi polynomial technique is then used to solve the integral equations numerically. The stress intensity factors are provided. The stress intensity factors have been calculated numerically and displayed graphically.

The interface crack problems of a laminated piezoelectric plate under a state of generalized plane deformation have been studied within the anisotropic theory. The method of Fourier transforms and the stiffness matrix formulation have been employed and the problem has been reduced to the solution of a system of singular integral equations. The stress and induction intensity factors have been provided, and have been calculated numerically and displayed graphically.

After the Hamilton principle for thermo-mechanical electric coupling problem is derived, the third-order shear deformation theory is extended to encompass piezothermoelastic laminated plates. Based on the velocity feedback control, a model for the active vibration control of laminated plates with piezothermoelastic sensor: actuator is established. An analytical solution is obtained for the case of general forces acting on a simply supported piezothermoelastic laminated plate. Numerical results are presented. The factors that influence the controlled responses of the plate are examined.

Using the extended version of Eshelby-Stroh's formulation and the method of analytical continuation, the problems of interface cracks are reduced to a Hilbert problem of vector form. A general explicit closed form solution for piezothermoelastic interface crack problem is then obtained, the whole field solutions of temperature, heat flux, displacements, electric field, stress and electric induction are given, the explicit expressions for the crack opening displacements and electric potential are also provided. A solution is obtained for the interaction problem between the interface cracks and a point heat source.