Abstract
A crack in a plate of a functionally graded piezoelectric material mathematically modeled by a non-homogeneous solid is studied under transient thermal loading conditions. It is assumed that initially the medium is at the uniform temperature and is suddenly subjected to a uniform temperature rise along the one of the traction-free boundaries. The crack faces are supposed to be completely insulated. Some material properties are assumed to be exponentially dependent on the distance from the crack line parallel to the boundaries of the plate. By using both the Laplace transform and Fourier transform, the thermal and electromechanical problems are reduced to a singular integral equation and a system of singular integral equations. The singular integral equations are solved numerically, and a numerical method is then employed to obtain the time dependent solutions by way of a Laplace inversion technique. The intensity factors vs. time for various material constants and geometric parameters are calculated.
