State-Space Approach for Energy Release Rate Analysis of Delaminated Laminates with Stiffeners

Based upon the interfacial spring-layer model, a state-space approach for the energy release rate analysis of stiffened laminates with a planar delamination was presented. The main advantages of the present method are that the same mesh is used for each layer, and only the so-called state variables at the top and bottom surfaces of structure in the final control equation of structures are involved. On the other hand, the oscillatory singular stresses around the delamination front are avoided as a result. Instead, stress resultant jumps are found in the sublaminate across the delamination front. Moreover, the technique accounts for the compatibility of displacements and stresses between layers and the transverse shear deformation in the control equation of structure. To avoid the possibility of material penetration phenomenon of the delaminated region, the unilateral frictionless contact interface is adopted in the interfacial spring layer between sublaminates. With the aid of the virtual crack closure technique, the accuracy of the method was assessed by comparing the results with existing examples. The effects of stiffeners on the distribution of the energy release modes I, II, and HI of the delaminated laminates with two stiffeners were analyzed by the present method.