Stiffness reduction of cracked general symmetric laminates using a variational approach

In this paper, stiffness reduction of general symmetric laminates containing a uniform distribution of matrix cracks in a single orientation is analyzed. An admissible stress field is considered, which satisfies equilibrium and all the boundary and continuity conditions. This stress field has been used in conjunction with the principle of minimum complementary energy to get the effective stiffness matrix of a cracked general symmetric laminate. Natural boundary conditions have been derived from the variational principle to overcome the limitations of the existing variational methods on the analysis of general symmetric laminates. Therefore, the capability of analyzing cracked symmetric laminates using the variational approach has been enhanced significantly. It has been shown that the method provides a rigorous lower bound for the stiffness matrix of a cracked laminate, which is very important for practical applications. Results derived from the developed method for the properties of the cracked laminates showed an excellent agreement with experimental data and with those obtained from McCartney’s stress transfer model. The differences of the developed model with McCartney’s model are discussed in detail. It can be emphasized that the current approach is simpler than McCartney’s model, which needs an averaging procedure to obtain the governing equations. Moreover, it has been shown that the existing variational models are special cases of the current formulation.