Interlaminar Stresses by Sing Method Based on Interpolation of the Highest Derivative

Computation of interlaminar stresses from one-dimensional equivalent-single-layer beam theories using the sinc method based on interpolation of the highest derivative is performed. The method is proposed to be an efficient tool for determining through-the-thickness variations of interlaminar stresses by the equilibrium equations of three-dimensional elasticity, because the required higher-order derivatives of displacements are accurately obtained without postprocessing, an improvement over presently used finite element methods. In functionally graded material, the sinc method offers additional benefits. Because the method employs numerical indefinite integration by double-exponential transformation, through-the-thickness integration can be performed numerically without computing additional integration weights. We obtain interlaminar stresses in symmetric cross-ply laminates and functionally graded sandwich composites using the sinc method based on interpolation of the highest derivative to approximately solve the static governing equations of the Timoshenko beam theory and the Bickford beam theory. Displacements and stresses from the present approach are compared with three-dimensional finite element method results obtained with ABAQUS/Standard. Our results indicate that the interlaminar stresses throughout the majority of the length of the beam are accurately approximated with the sinc method. The present results are significantly erroneous near the boundary because of three-dimensional edge effects not captured by the one-dimensional analysis.