Prediction of Interlaminar Stresses in Laminated Beams by Modified SIHD

Abstract

Computation of transverse shear and transverse normal stresses or interlaminar stresses from one-dimensional equivalent single-layer beam theories using Sinc Method based on Interpolation of Highest Derivative (SIHD) [Li, C. and Wu, X., Numerical Solution of Differential Equations Using Sinc Method Based on the Interpolation of the Highest Derivatives, Applied Mathematical Modeling, Vol. 31, 2007 pp. 1{9.] is preformed. SIHD, a form of the Sinc collocation method in which Sinc basis functions are used to approximate the highest derivative in the governing equation of the underlying boundary value problem, is proposed as an ecient method for determining through-the-thickness variations of interlaminar stresses by integration of the equilibrium equations of three-dimensional elasticity. Because the required higher-order derivatives of the displacements are obtained without post-processing, an improvement over presently used nite element based methods, SIHD is benecial for this application. In functionally graded material, SIHD oers additional benets. Because material properties may exhibit complicated variations through the thickness, determining transverse shear and normal stress components by integration of the threedimensional elasticity equations may become impossible to perform analytically. However, because SIHD employs numerical indenite integration by double exponential integration, the integration can be performed numerically without computing additional integration weights. In this paper, we obtain interlaminar stresses in symmetric cross-ply laminates and sandwich composites with functionally graded material using SIHD to approximately solve the static governing equations of the Timoshenko beam theory (FSDT), and Bickford’s consistent higher order beam theory. We compare stresses, including interlaminar stresses, and displacements for various thickness-to-length ratios obtained from SIHD with an approximate solution of three-dimensional elasticity obtained using the nite element method by ABAQUS/Standard. Our results indicate SIHD accurately approximates the interlaminar stresses throughout the majority of the length of the beam; however, near the boundary, our results are signicantly dierent