A special boundary element for holes/cracks in composite laminates under coupled stretching-bending deformation

Recently, we corrected the Green's functions for holes/cracks in composite laminates under coupled stretching-bending deformation. Through these corrected Green's functions, the fundamental solutions required for the special boundary element of holes/cracks in composite laminates are derived. By the use of dual coordinates, the derived fundamental solutions can be further applied to the cases of inclined holes and cracks. Moreover, a formula evaluating the stress intensity factors by using boundary nodal displacements and tractions is derived. With these closed-form solutions, the special boundary element developed in this study can deal with various kinds of hole/crack problems in composite laminates. Their loads can be in-plane tension, compression, or shearing, out-of-plane force, bending or twisting, distributed or concentrated, on the surfaces or along the edges; their boundaries can be simply supported, clamped, or free edges; their defects can be a hole or a crack with horizontal or inclined orientation; their laminates can be symmetric or unsymmetric. No matter which kind of conditions, no meshes are required on the hole and crack surfaces. And the stress intensity factors of cracks can be calculated directly without requiring any meshes along the crack surfaces or near the crack tip.