On the analysis of multiple site damage in stiffened panels

The analysis of stiffened panel structures containing multiple site damage is addressed through the stress function method, in association with the requirement for displacement compatibility between the stiffeners and the panel. The problem reduces to a system of simultaneous equations that is solved for the unknown forces at the stiffener attachment points. The multiple site damage is represented as a series of arbitrary straight collinear cracks, which are incorporated directly into the stress and displacement field expressions by adopting the complex variable formulation of plane elasticity developed by Muskhelishvili. This approach removes the need to model any of the crack surfaces, since the boundary conditions on each of the cracks are satisfied implicitly, and avoids the necessity for iterative solution procedures such as the alternating method. Nevertheless, the presence of multiple cracks demands that the stress and displacement fields are evaluated through Gaussian quadrature, although this requirement is circumvented in some cases by developing series expressions for the integral.The effect of plasticity in both unstiffened and stiffened panels with multiple collinear cracks is included using the strip yield model of Dugdale and Barenblatt. In general, the size of the plastic zone at each crack tip is not known a priori, and the ensuing nonlinear system equations are solved numerically. However, the system equations become linear in the special case where crack tip plasticity is omitted from the analysis, and a direct solution is possible. The accuracy of the approach is established by comparing the crack tip opening displacements and plastic zone sizes, or the stress intensity factors in a linear analysis, with known results. New results are also obtained for strip yield cracks in a stiffened panel containing multiple site damage.Finally, the stress intensity factor solution for multiple cracks is used to assess the residual strength of a thin unstiffened sheet with multiple site damage, using the established R-curve method. The fracture strength of the panel is also calculated with an estimate of the J-integral, which is derived from the stress intensity factor solution through a scheme proposed by Ainsworth.