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Contact problems can be converted into the spatial frequency domain using Fast Fourier Transform (FFT) techniques. Spectral analysis is used to develop an algebraic relationship between the surface displacement and the contact pressure. This relationship can be used to find the contact pressure or displacement for the contact of smooth surfaces or the complete contact of rough surfaces. In addition to providing rapid, robust solutions to contact problems, the algebraic relationship contains details of the relationship between surface displacement and contact pressure on different length scales. In particular, it is shown that the frequency composition of pressure is similar to that for slope of the surface displacement. Thus, the high frequency content of the surface profile gives rise to high localized contact pressure, in some cases singular pressure for complete contact. However, measurement limitations always lead to the omission of certain high frequency components of the surface profile. Assuming that the high frequency content of the surface profile obeys a power law, spectral analysis is also used to estimate partial contact parameters. This result relates the exponent of the power law to the contact pressure and implied surface integrity. It is concluded that spectral analysis can be combined with the FFT to provide a useful technique for classifying rough surface contacts.

The onset of widespread fatigue damage in riveted aircraft structure has been linked to sharp gradients of stress arising from contact between rivets and rivet holes. In addition, the mechanics of load transfer in lap joint structure (and resulting damage) is in uenced by the through-thickness restraint offered by the installed rivet. Finally, the propagationof fatigue cracks at and around the rivet/hole interface is tied to the residual stress eld induced during the riveting process. In light of the in uence that rivet installation has on the fatigue performance of riveted joints, the aim was to link details of a quasi-static, squeeze force-controlled riveting process as provided by nite element modeling to the resulting residual stress eld in a single-lap joint structure. Supporting experiments provide insight into the inelastic response of the rivet material and validation of the model results. These results from the model reveal both a strong through-thickness gradient in residual stresses and a change in the distribution of residual hoop stress near the rivet/hole interface with squeeze force. Comments are also made regarding the relationship between riveting process parameters and trends in observed fatigue failures of riveted lap joint test articles.