High-Order Layerwise Formulation of Transverse Shear Stress Field for Laminated Composite Beams

Abstract

This paper presents a high-order layerwise theoretical framework for laminated composite beams based on a piecewise description of the transverse shear-stress field. Linear and quadratic variations in the transverse shear-stress field are assumed in each discrete layer, and compatibility conditions of the shear stress are a priori fulfilled through the introduction of shear-stress variables defined on the layer surfaces. Based on the stress–strain relations, the transverse shear strain is obtained, and the in-plane displacement is determined by integrating the transverse shear strain along the thickness direction. By imposing continuity conditions of the displacements, a displacement field expression that contains only displacement variables is formulated. Moreover, a two-node beam element associated with the present model is developed, where Hermite cubic interpolation functions are used for the transverse displacement variable, and linear interpolation functions are employed for the remaining displacement variables. Comparisons with the exact solution, various displacement-based theories, and high-fidelity finite element models demonstrate the high accuracy of the present model in predicting the stress and displacement distributions. In addition, the introduction of sublayers to improve the modeling accuracy and the influence of the stiffness ratio between layers on the effectiveness of the proposed model are addressed.