Correction of the existing solutions for hole/crack problems of composite laminates under coupled stretching-bending deformation

For unsymmetric composite laminates under in-plane forces, transverse loads, out-of-plane bending and/or twisting moments, the stretching and bending deformations would be both induced and coupled together. Through Stroh-like formalism for coupled stretching-bending analysis, several analytical solutions for holes/ cracks in laminates were presented in the literature. However, due to the improper use of traction-free hole boundary conditions, most of the existing solutions provide wrong solutions and their associated deflections evaluated by numerical integration of slopes have the multi-valued problem. By revising the traction-free hole boundary condition and setting the single-valued requirement for deflection, some existing solutions are corrected in this paper. The considered problems of holes/cracks in laminates include the one (1) under uniform stretching and bending moment, (2) under uniform heat flow in thickness direction, (3) for electro-elastic laminates, and (4) for Green's functions with concentrated forces and moments in three orthogonal directions. We not only provide the corrected solutions, but also derive the explicit closed-form solutions of deflection for the above mentioned problems. Additionally, with the corrected Green's functions, a special boundary element method is developed to assist the verification of corrected solutions and to show its accuracy and efficiency on the problems with holes/cracks in laminates.