pline variational three dimensional stress analysis of laminated composite plates with open holes

Independent polynomial spline approximation of displacement and interlaminar tractions is proposed for stress analysis in laminates with open holes. Spline approximation eliminates the inter element compatibility problems leading to unsatisfactory finite element results in the presence of field singularities. Spline approximation offers continuity of displacement, strain and stress fields within homogeneous domains preserving, at the same time, the advantages of local approximation, such as sparsity of the resulting system of equations. Three dimensional full field solution is obtained. Converged stresses and consistent boundary conditions, such as interlaminar traction continuity, are displayed. A closed form asymptotic solution, valid in the vicinity of the hole edge at the interface of two orthotropic plies of arbitrary thickness has been developed to verify the spline approximation based full field solution. Excellent agreement has been observed for interlaminar stresses in a [45/-451, AS4/3501-6 laminate under uniaxial tension. The polynomial spline approximation, ideally suited for problems concerned with the singular solution behavior, has been applied to three dimensional stress analysis in practical composites containing tens of plies