Based on beam-shaped-function, the analytical solution for composite plates with arbitrary embedded delaminations is presented. The deflection function of the delaminated plate is composed by those of beams with the corresponding loading and support conditions, which can be easily and accurately derived from the beam analysis, and the deflection amplitude is derived by the minimum potential energy principle. The closed form solutions of displacements, stresses, and energy release rate of a composite plate containing an arbitrarily embedded rectangular delamination are obtained and compared with the three-dimensional finite element results to validate the accuracy of this present method. Furthermore, the influences of delamination depth, length, central position, and modulus mismatch ratio (E 1 /E 2 ) of the upper and lower sublaminate on the energy release rate are discussed.

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A two dimensional beam model is proposed for delamination analysis of composite laminates, where Timoshenko's plane cross-section assumption is abandoned, and the longitudinal displacement of the beam is proposed as continuous functions of the transverse and the longitudinal coordinates, to match shear deformations. Moreover, the composite laminate is modeled as upper and lower sub-beam through the delamination interface, and corresponding conditions for interface sliding are satisfied through a generalized variational theory. The accuracy of the results of this analytical model is verified by comparison with those from three dimensional finite element models. Furthermore, the influences of delamination depth, length, central position and modulus mismatch ratio (E1/E2) of the upper and lower sublaminate to the energy release rate are discussed.