A generalized plane-strain theory for transversally isotropic plates

By adopting Kane and Mindlin's assumption,that the through-the-thickness extensional strain is uniform through the plate thickness, a generalized plane-strain theory is developed for transversely isotropic plates. The three-dimensional governing equations are successfully reduced to two coupled equations in the two-dimensional space. With the new theory, explicit solutions of the three-dimensional stresses, especially the through-the-thickness component, around a circular hole and a V-shaped notch in a transversely isotropic plate of arbitrary thickness are derived. The analytical solutions are verified by comparing with finite element results.