On the use of quasi-dynamic modeling for composite material structures: Analysis of adhesively bonded joints with midplane asymmetry and transverse shear deformation

Abstract

Adhesively bonded joints offer an attractive alternative to bolted/riveted approaches to joining load bearing elements because of potential weight savings and enhanced joint strength efficiency. However, modeling of these joints including substrate asymmetry, anisotropy, thickness variation, transverse shear deformation, hygrothermal growth, and complicated models for the adhesive layer can prove to be very unwieldy. This paper presents a solution methodology to model adhesively bonded joints which is capable of handling these important effects. The differential equations of motion are modified to include fictional damping type terms. Using a modified form of the thin structural displacements including temporal variation, the quasi-dynamic governing equations for thin plates are developed. The plate relationships are simplified to yield the quasi-dynamic beam/rod relationships. An assortment of boundary and initial conditions in terms of displacements are included for completeness and to facilitate implementation. To acquire quantitative solutions, the quasi-dynamic relationships are recast into the form of finite difference equations. A form suitable for the solution of a wide range of practical problems is presented. For completeness, the boundary and initial conditions are also recast into finite difference form. Justification of the choice to include the fictional damping terms and the discrete solution methodology is presented. The discrete governing equations are verified using the classical cantilevered beam case. Deviations from the classical solution resulting from the inclusion of transverse shear deformation and solution convergence are discussed. Once the quasi-dynamic solution methodology is validated, the single lap shear joint is modeled. Finally, a parametric study is performed to determine the influence of asymmetric adherend stiffness property variations on the peel and shear stresses in the adhesive layer. It is observed that decreases in adherend lumped shear stiffness results in reductions in the adhesive layer stress peaks. It is also observed that asymmetrically constructed adherends are of potential benefit to the reduction of adhesive peel stresses.