A unified approach to geometrically nonlinear analysis of tapered bonded joints and doublers

A unified approach for approximating the adhesive stresses in a bond line of a tapered bonded joint or doubler is delineated within the framework of a geometrically nonlinear analysis. The approach follows the Goland–Reissner solution method for a single-lap joint and involves a two-step analysis procedure. The approach also allows for the analysis of a tapered bonded joint and doubler with non-identical adherends. In the first step of the procedure, the two adherends are assumed to be rigidly bonded, and the nonlinear moment distribution along the joint is determined. Since the bending moment solution in this step is simple, it will be derived in closed-form using elementary functions. In the second step analysis, only the overlapped area of the joint is considered with the nonlinear bending moments obtained from the first step at the end of the overlap prescribed as one of its boundary conditions. This latter problem is then solved by using the multi-segment method of integration [Kalnins, A., 1964. Analysis of shell of revolutions subjected to symmetrical and non-symmetrical loads. Journal of Applied Mechanics 31, 1355–1365]. In contrast to the original Goland–Reissner solution method [Goland, M., Reissner, E., 1944. The stresses in cemented joints. Journal of Applied Mechanics 11, A17–A27], the second step analysis can be conducted within both geometrically linear theory and an approximate geometrically nonlinear theory