Stress analyses around holes in composite laminates using boundary element method

Abstract

A three-dimensional (3D) boundary element method (BEM) is developed for the analysis of composite laminates with holes. Instead of using Kelvin-type Green's functions of anisotropic infinite space, 3D layered Green's functions with the materials of each layer being generally anisotropic, derived recently in the Fourier transform domain, are implemented into a 3D BEM formulation. A novel numerical algorithm is designed to calculate layered Green's functions efficiently. It should be noted that since layered Green's functions satisfy exactly the continuity conditions along the interfaces and top and bottom free surfaces a priori, the model becomes truly 2D and discretization is only needed along the hole surface and prescribed traction and/or displacement boundaries. To test the validity and accuracy of the proposed method, the present layered BEM formulation is applied to the problem of an infinite anisotropic plate with a circular hole where the analytical solution is available. It is found that even with a very coarse mesh, the present BEM can predict the hoop stress very accurately along the hole surface. The BEM formulation is then applied to analyze two composite laminates (90/0) s and (−45/45) s, under a remote in-plane strain, that have been studied previously with different approaches. For the (90/0) s case, the hoop stresses along the hole surface predicted by the present layered BEM formulation are in very close agreement with the previous results. For the (−45/45) s case, however, it is found that a nearly converged solution (less than 5% convergence by doubling the mesh) by the present method is at significant variance with the previous ones that are lack-of-convergence checks. It can be expected that for designing the bolted joints of composites with many layers, a computational tool developed based on the present techniques would be robust and offer a much better solution with regard to accuracy, versatility and design cycle time.