Complex Variable Method for Problems of a Laminate Composed of Multiple Isotropic Layers

Abstract

A new method of the analysis of a plate composed of thin layers of isotropic linear elastic material is developed. A general solution for displacement, resultant stress and resultant moment fields is obtained by using the complex function theory. It is proved that the complete solutions of the laminated plate subjected to tractions prescribed on its boundary can be obtained from the sum of solutions for uncoupled plates. Particular attention is devoted to the crack tip field and energy release rate for the laminated plate. A closed form solution for singular fields near the crack tip and the relation between the J-integral and the intensity factors are derived through the complex potential formula. Complete forms of the complex potentials for 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.