Variable Kinematics Layerwise Model for Analysis of Bonded Joints

Abstract

A displacement-based multi-layered zig-zag plate model with variable in-plane and through-the-thickness representation and fixed degrees of freedom is developed for analysis of bonded joints with laminated adherents. Characteristic feature, the in-plane representation can be varied across the adherents and the overlap to better simulate the variation of solutions and to satisfy the stress boundary conditions at the ends of the overlap. To this purpose, continuity functions are incorporated enabling the continuity of displacements and stresses where the representation is changed. Other continuity functions are included to allow an a priori fulfillment of the out-of-plane stress contact conditions at the interfaces of adjacent layers. High-order, through-the-thickness contributions are incorporated allowing the representation to be refined where step gradients rise. As the representation can vary from point to point, the present model permits an accurate analysis of laminates with general boundary conditions and of bonded joints under a unified approach. Applications are presented to sample cases of single- and double-lap joints taken from the literature. Specifically, three single-lap joints are considered, two of which with aluminum adherents and one with laminated composite adherents. Also a double-lap joint with aluminum adherents is analyzed. The numerical results show that accurate stress predictions are obtained with a low computational effort in all the cases considered using appropriate series expansions of displacements. The accuracy is good even using a single component in the expansion, which implies solving a 3x3 system.