A simplified method for the geometrically nonlinear analysis of the single lap joint

A simplified method for the geometrically nonlinear analysis of the single lap joint is presented. The method consists of first finding the force/moment boundary conditions at the joint overlap ends. This is achieved by solving the differential equations that relate the resulting moment to the applied load and the unknown transverse deflection. The solution for the deflection is eventually reduced to the solution of a system of six linear equations in six unknown coefficients. Once the force/moment boundary conditions for a given load are known, a linear finite element analysis is used to find the joint stresses using only the overlap region of the joint. Since in many practical joints adhesive fillets exist at the ends of the overlap, the existence of these fillets is taken into account in the formulation. Also, to allow for various support conditions of the grips of the testing machine, solutions are presented for both simply supported and clamped-clamped end supports. Additional boundary conditions on the linear finite element model using multipoint constraints are also given that allow consideration of only one half of the overlap length in the analysis. This is possible due to the inherent conditions of antisymmetry that exist between the top and bottom of the joint overlap. The accuracy of the simplified method was verified by comparison of results against a full-size geometrically nonlinear finite element model, and it was found that the results were very close, within 3%. Overall, the method results in considerable savings in both solution time and modeling effort, while maintaining accuracy.