Complex variable method for problems of a laminate composed of multiple isotropic layers

A new method of the analysis of a plate composed of thin layers of isotropi c linear elastic material is developed. A general solution for displacement , resultant stress and resultant moment fields is obtained by using the com plex function theory. It is proved that the complete solutions of the lamin ated plate subjected to tractions prescribed on its boundary can be obtaine d from the sum of solutions for uncoupled plates. Particular attention is d evoted to the crack tip field and energy release rate for the laminated pla te. A closed form solution for singular fields near the crack tip and the r elation between the J-integral and the intensity factors are derived throug h the complex potential formula. Complete forms of the complex potentials f or a crack in an infinite laminate as well as for the singularities such as a point force, a point moment and a dislocation are also obtained.