Macroscopic Finite Element for a Single Lap Joint

*† Macroscopic finite elements are elements with an embedded analytical solution used to carry out efficient, mesh independent finite element analysis. In the present study, this method of macro elements was applied to a single lap joint. The adherends were modeled as Euler-Bernoulli beams, and the adhesive layer assumed to be in a state of plane stress. The field equations were derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields were used to generate shape functions and a stiffness matrix for a single finite element. Simplifying assumptions incorporated in the model development were evaluated by comparing with several corresponding 2-D finite element models with different joint parameters. The results showed that the derived macroelement results in considerable cost savings in computational modeling of structural systems that contain multiple lap joints.