Analytical-generalized variational method of solution for delaminations of laminates

The delamination solution of composite laminates, orthogonally and symmetrically stacked and subjected to longitudinal tensile forces, is given. First of all, the eigen function expansions of stress and displacement fields, satisfying all of the basic equations, boundary conditions on crack (delamination) surfaces and conditions of continuities between different plies are derived. Then, the stress intensity factors as the leading terms in the above expansions are determined by the generalized variational principle for multi-regions, to satisfy the boundary conditions, excluding those along the crack surfaces satisfied previously. There are only line integrals in the variational equations due to the previous satisfaction of all basic equations. The computations show that this method of solution has the advantages of simple programming and rapid convergence, and is time-saving.