On the application of finite element techniques in the displacement compatibility method

Abstract The displacement compatibility method was used by Poe, Swift and others, to evaluate the stress intensity factor in stiffened panels with cracks. In the displacement compatibility method as they used it, the deformations of both the skin and the stiffening elements have been defined with flexibility matrices. In this paper, the governing equations are modified such that the stiffener deformations are described with a stiffness matrix. For the stiffeners, it is more convenient to use a stiffness matrix than a flexibility matrix. The stiffness matrix can be defined with finite element techniques, allowing a wider range of options to model the stiffeners. Such options include the modelling of the finite width of stiffeners, plastic deformations and geometrically non-linear deformations. It is shown that the solution obtained with the modified governing equations is identical to the solution of Poe and Yeh for elastic panels, and comparable to the solution of Creager and Liu for panels with perfectly plastic strips. The computer time required to solve the modified equations is not increased significantly, compared to the original equations. As an example of an application of the modified equations, Creager and Liu's panels have been analysed using the net-section yield failure model of Gunther and Wozumi for riveted stiffeners. In the present modified governing equations, the stiffeners might retain their complexity known from a full finite element analysis, without significantly increasing the computer time required for a parametric study.