Green’s Functions for Holes/Cracks in Laminates With Stretching-Bending Coupling

Abstract

Consider an infinite composite laminate containing a traction-free elliptical hole subjected to concentrated forces and moments at an arbitrary point outside the hole. This problem for two-dimensional deformation has been solved analytically in the literature, while for the general unsymmetric composite laminates stretching and bending coupling may occur and due to the mathematical complexity the associated Green’s functions have never been found for complete loading cases. Recently, by employing Stroh-like formalism for coupled stretching-bending analysis, the Green’s functions for the infinite laminates (without holes) were obtained in closed-form. Based upon the nonhole Green’s functions, through the use of analytical continuation method the Green’s functions for holes are now obtained in explicit closed-form for complete loading cases and are valid for the full fields. The Green’s functions for cracks are then obtained by letting the minor axis of ellipse be zero. By proper differentiation, the stress resultants and moments along the hole boundary and the stress intensity factors of cracks are also solved explicitly. Like the Green’s functions for the infinite laminates, only the solutions associated with the in-plane concentrated forces f⁁1,f⁁2 and out-of-plane concentrated moments m⁁1,m⁁2 have exactly the same form as those of the corresponding two-dimensional problems. For the cases under the concentrated force f⁁3 and torsion m⁁3, new types of solutions are obtained.